Related-Party Transaction Networks and Corporate Credit Risk in Complex Financial Systems: Evidence from Network Characteristics and Local Configurations

Highlights

Please indicate how your work links to systems science via your contributions to systems practice, theory, and/or methodology.

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The study represents disclosed RPTs as annual weighted bipartite networks, preserving transaction content and shared-counterparty structures within a complex financial system.

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The framework distinguishes focal-firm network characteristics from local configurations, linking two complementary levels of a complex transaction system.

What are the main findings and/or the implications of the main findings?

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Firm-level RPT attributes display a double-edged pattern: relational scale and projected reach are associated with thinner credit buffers, whereas concentration among core counterparties can coincide with a larger KMV buffer.

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Repeated closed 2 × 2 sharing, rather than coarse degree-based configurations, is the principal local microstructure associated with thinner structural credit buffers.

Abstract

Firms are embedded in transaction systems whose organization can generate both coordination benefits and relational exposure. Using disclosed related-party transactions (RPTs), we construct annual weighted bipartite networks for 2674 Chinese A-share listed firms and examine 26,264 RPT-active firm-year observations from 2003 to 2024. The analysis distinguishes three firm-level dimensions—relationship scale, transaction concentration, and projected shared-counterparty position—from local bipartite microstructures. The firm-level evidence reveals a double-edged pattern: broader and more valuable RPT relationships are associated with lower Merton and KMV distance to default (DD), and projected degree is associated with lower Merton DD, whereas a higher top-three-related-party share is associated with higher KMV DD. Direction-specific estimates reinforce this distinction. Scale is negatively associated with DD on both the seller/provider and buyer/recipient sides, concentration is generally positive (especially on the buyer/recipient side), and seller/provider projected degree is negatively associated with KMV DD. At the local level, closed 2 × 2 presence and intensity are negatively associated with Merton DD, while simple degree-based forms and shared-counterparty bridges provide less stable differentiation. Observed closure substantially exceeds degree-sequence-preserving randomized benchmarks, and excess closure remains negatively associated with Merton and Bharath–Shumway DD after relationship opportunities and counterparty popularity are controlled. The results establish transaction scale, value allocation, projected reach, and repeated local sharing as complementary signals for structure-sensitive credit risk monitoring in complex transaction systems.

1. Introduction

Corporate credit risk is conventionally assessed using information on assets, liabilities, profitability, cash flows, and market valuation. These fundamentals remain essential, but recurring transactions, counterparty quality, contingent obligations, and interfirm organization may affect debt-servicing capacity before their consequences are fully reflected in conventional indicators. A systems perspective therefore treats the firm as a participant in an evolving network of embedded economic exchanges and relates firm-level risk to the breadth, intensity, position, and local organization of those exchanges [1,2,3,4].

Related-party transactions (RPTs) make these interfirm relationships observable. Business-group affiliations, concentrated ownership, and multi-tiered control structures are common in the Chinese A-share market. Listed firms maintain recurring relationships with related parties through purchases and sales, intercompany financing, asset transfers, guarantees and collateral arrangements, and service provision. Unlike ownership links or interlocking-director ties, RPT links represent disclosed transactions or commitments involving funds, goods, assets, or services. Because they involve identifiable economic activities, these links can affect cash flow stability, resource allocation, and debt-servicing capacity. Annual disclosures also allow these relationships to be reconstructed as time-varying weighted networks rather than treated solely as isolated transactions.

The credit risk consequences of RPTs depend on how the transactions are organized and governed. Internal capital market theory suggests that well-governed intragroup transactions can reallocate funds and operating resources, alleviate financing frictions, and support continuity [5,6]. Agency theory emphasizes appropriation through unfair pricing, non-operating fund occupation, or asset transfers when information asymmetry is pronounced and governance is weak [7,8]. Transaction purpose, benefit flows, counterparty quality, and structural conditions therefore matter; aggregate transaction value alone cannot distinguish these conditions.

Transaction network studies show that local payment network topology and observed interfirm financial transactions contain credit risk information and may improve rating or default prediction [9,10]. These findings establish the relevance of relational transaction data, but they do not resolve what is distinctive about related-party transactions. RPT links are shaped by ownership, control, internal capital markets, guarantees, and transfers within business groups; the same party can therefore represent support, dependence, contingent obligation, or tunneling. The finance contribution must consequently be evaluated by whether RPT network measures add information beyond aggregate activity and conventional controls and by whether shared-party structures retain meaning after relationship opportunities are held fixed.

The study asks whether the scale, value distribution, projected position, and local organization of disclosed RPT relationships are associated with firm-level credit buffers among RPT-active listed firms and whether local closure retains information after observable relationship opportunities are controlled.

The findings reveal two complementary features of RPT organization. Across the three firm-level indicator classes, relational scale and projected shared-counterparty reach are associated with thinner credit buffers, whereas concentration among core counterparties can coincide with a larger KMV buffer. At the local level, repeated closed 2 × 2 sharing is the most informative microstructure after relationship opportunities are benchmarked. Together, these results emphasize the double-edged character of RPT embeddedness rather than treating network connectedness as uniformly beneficial or harmful.

The study makes three contributions derived directly from these gaps. First, it develops an RPT-specific transaction network framework that distinguishes relationship scale, transaction concentration, and projected position, revealing the double-edged credit risk content of direct and shared-counterparty relationships. Source-coded seller/provider and buyer/recipient models extend this three-dimensional framework by showing how relational expansion, value concentration, and projected reach vary across transaction roles. Second, the analysis preserves local bipartite microstructures and shows that repeated closed 2 × 2 sharing contains information beyond aggregate RPT activity, focal degree, counterparty popularity, and the two-sided degree sequence. Third, it advances a firm-level systems perspective by demonstrating how transaction value allocation and local organization provide complementary screening signals for creditors, auditors, regulators, and firms operating within complex financial systems.

The remainder of the paper reviews the relevant literature and develops the hypotheses, describes the network construction and empirical design, reports the findings for the two analytical dimensions, and concludes with implications for relationship-based risk governance in complex financial systems.

2. Literature Review and Hypothesis Development

2.1. Related-Party Transactions, Corporate Networks, and Credit Risk

Related-party transactions (RPTs) are exchanges between a firm and parties connected through ownership, control, managerial arrangements, or other economic relationships [11]. They include loans, guarantees, purchases and sales, asset transfers, service provision, and cost allocation and can affect operating cash flows, asset quality, and debt obligations. These implications are especially relevant in China, where concentrated ownership and business group control remain common. Controlling shareholders and group members may use internal resources to support listed firms, but control and informational advantages may also facilitate transfers away from them [8,12,13,14].

Two established perspectives explain these contrasting outcomes. Internal capital market theory argues that business groups can use control rights and superior internal information to allocate funds and operating resources, ease financing frictions, and maintain continuity [5,6,15,16]. Agency theory emphasizes the separation of control and cash flow rights: weak governance and monitoring can allow unfair pricing, fund occupation, benefit transfers, and risk shifting [7,8,17]. The allocation-versus-rent-seeking tension follows the classic internal capital market distinction between efficient internal financing and divisional influence costs [18,19]. An RPT’s consequences therefore depend on its purpose, benefit allocation, counterparty characteristics, and governance conditions.

Relational transaction data are already known to contain credit risk information. Letizia and Lillo [9] connect local topology in a large Italian corporate payment network to credit ratings, while Vinciotti et al. [10] show that observed UK interfirm financial transactions improve default-risk models. Production network evidence further shows that the economic content and substitutability of links shape shock transmission [20]. The RPT setting differs because links arise within disclosed ownership-, control-, and influence-based relationships and can include loans, guarantees, asset transfers, purchases, sales, and services. This institutional content makes it necessary to distinguish relationship breadth, economic value, and transaction type rather than interpret an edge as a homogeneous exposure.

Creditors may also respond to organizational and reporting arrangements when their rights or recovery prospects change; Hamdani et al. [21], for example, document bond price and reporting responses to an expansion of creditors’ bankruptcy initiation rights. In the present setting, creditor relevance arises from whether disclosed RPT organization provides incremental information about structural DD after standard financial controls, aggregate RPT activity, and observable network opportunities are considered.

2.2. Network Characteristics and Credit Risk Implications

Relational scale captures the breadth and financial importance of a firm’s direct ties. A larger set of counterparties may broaden access to information and resources, yet it also increases contractual, pricing, settlement, and monitoring tasks and exposure to counterparty-specific conditions [22,23,24]. Greater breadth can also increase structural complexity and the coordination burden associated with upstream relationships [25]. The number of related parties, total RPT amount, and average amount per related party distinguish relationship breadth, aggregate resource commitment, and the financial intensity of a typical tie.

Transaction concentration describes how RPT value is distributed across counterparties. Concentrated relationships can support repeated cooperation, relationship-specific investment, and more predictable resource coordination. They may also create dependence if the loss or deterioration of a key counterparty has a disproportionate effect on operations and cash flows [26,27,28]. Four measures are retained because they emphasize different aspects of the distribution: the Herfindahl–Hirschman Index (HHI), the largest-related-party share, the top-three-related-party share, and a nonlinear dependence index.

Network position captures a firm’s location relative to other participants. Central firms may have broader access to information and resources, but they may also be exposed to a wider range of operating environments and face more complex monitoring and responsibility allocation [22,29,30]. In the projected interfirm network, degree centrality records immediate connections created by shared related parties, whereas closeness centrality measures broader reachability through short paths. Direct counterparty count and projected interfirm position are related but conceptually distinct.

2.3. Local Network Configurations

Node-level characteristics do not fully describe how relationships are arranged within a firm’s immediate environment. Local configurations can preserve information beyond dyadic ties, although their frequency depends on focal-firm degree, counterparty popularity, and network coverage. We therefore evaluate closed 2 × 2 participation against continuous opportunity controls, degree–volume reweighting, counterparty average and maximum degree, hub-downweighted projection, identifier-only networks, exclusions of obvious parent–subsidiary and same–parent edges, and 100 degree-sequence-preserving randomizations of each annual bipartite graph. These benchmarks separate repeated sharing implied by formation opportunities from observed excess closure.

Basic configurations discretize direct relationship breadth: a single-link configuration connects the listed firm to one related party, an open V-shaped configuration to two, and a star to three or more. Complex configurations retain shared nodes and repeated connections. Treating recurring small subgraphs as analytical objects follows network motif and supply network triad research [31,32,33]. A shared-counterparty bridge is supported by one common related party, whereas a closed 2 × 2 configuration occurs when two listed firms repeatedly share at least two related parties. Bridging and closure can support information access or verification but may also create common exposure, redundancy, or lock-in [34,35,36].

Each dimension captures a different monitoring problem. Scale measures the number and economic weight of ownership-linked relationships; concentration describes how transaction value is allocated across core counterparties; projected position captures indirect reach through shared parties; and closed 2 × 2 structure identifies repeated sharing within a local neighborhood. Repeated sharing may aid verification and coordination, but it may also concentrate common exposure and blur responsibility. Governance quality and transaction content determine which side of each trade-off dominates; the empirical coefficients are therefore interpreted as conditional net associations rather than deterministic mechanisms.

A bipartite representation preserves listed-firm and related-party roles and records disclosed transaction value on each annual edge. Its unweighted one-mode projection connects listed firms that share at least one related party, while compressing the number and economic value of shared parties and giving popular counterparties a potentially larger influence. Multilayer research represents interaction types as separate layers and allows layer-specific or cross-layer processes [37,38]. Building on this perspective, the present study retains the annual bipartite network as its primary representation and reconstructs transaction-type and role-specific subnetworks for heterogeneity analysis; a directed multiplex RPT model offers a natural extension for integrating contractual and legal layers.

2.4. Literature Synthesis and Research Gaps

Three gaps guide the analysis. First, the credit risk content of generic payment and interfirm transaction networks is established [9,10], but the incremental information in RPT networks shaped by ownership, control, guarantees, and internal capital markets is less clear. Second, local bipartite closure can be mechanically generated by relationship breadth and shared-party popularity, so its incremental content must be benchmarked against continuous scale and formation opportunities. Third, long-horizon RPT networks depend on disclosure coverage and entity resolution; temporal comparability and sample conditioning must therefore be explicit.

To address these issues, we estimate the nine continuous characteristics separately and use parsimonious joint models to assess overlap. Closure is evaluated within degree-volume cells, with opportunity controls, and against annual degree-preserving randomizations. Direction codes, counterparty IDs, relationship codes, and counterparty degree are then used for targeted sensitivity tests. Exact adjacent-year lags, two-way clustering, multiple-testing corrections, period subsamples, within-year ranks, economic magnitude calculations, and holdout prediction provide additional robustness checks.

2.5. Hypothesis Development

The literature does not support a uniform prediction for RPT connectedness. The expected association depends on whether a measure captures relational expansion, the distribution of transaction value, indirect reach through shared counterparties, or the local organization of those relationships. The hypotheses and research questions are organized by these structural dimensions.

In terms of network scale, a larger number of related parties broadens the range of relationships that the firm must govern. Greater total RPT value raises the weight of related transactions in cash flow and resource allocation, while a higher average amount increases the financial significance of a typical relationship. Although expansion may improve resource access, RPT counterparties may remain linked through ownership or control and need not provide the diversification of independent arm’s-length ties. Coordination costs, fund occupation opportunities, and counterparty exposure are expected to dominate.

Hypothesis 1 (H1).

A larger number of related parties, a greater total RPT amount, and a higher average RPT amount per related party are associated with lower corporate distance to default.

Regarding transaction concentration, concentration has competing implications. If a high HHI, largest-related-party share, top-three-related-party share, or dependence index reflects reliance on key counterparties and limited substitutability, interruption or opportunism may reduce cash flow stability and DD. If the same measures instead reflect stable, well-governed relationships, repeated exchange may improve information, resource matching, and predictability. Because the concentration measures do not by themselves identify which condition prevails, competing hypotheses are appropriate.

Hypothesis 2a (H2a).

When transaction concentration reflects structural dependence on key related parties, higher HHI, largest-related-party share, top-three-related-party share, and dependence index are associated with lower corporate distance to default.

Hypothesis 2b (H2b).

When transaction concentration reflects stable relationships and resource coordination, higher HHI, largest-related-party share, top-three-related-party share, and dependence index are associated with higher corporate distance to default.

Regarding projected network position, projected degree centrality indicates connections to a larger set of listed firms through common related parties, while projected closeness centrality indicates broader reachability through short paths. These positions may provide information and resources, but they also place the firm within a wider set of shared transaction environments and complicate monitoring and responsibility allocation. The exposure and governance channels are expected to dominate in the RPT setting.

Hypothesis 3 (H3).

Higher projected degree centrality and projected closeness centrality are associated with lower corporate distance to default.

In terms of local configurations, the single-link, open V-shaped, and star categories primarily discretize direct counterparty count. Because additional counterparties may expand resources while increasing coordination demands, their net association is left open. A closed 2 × 2 configuration is substantively different: repeated sharing creates cross-exposure and may make cash flow arrangements and responsibility boundaries harder for external capital providers to assess. A shared-counterparty bridge may be informationally useful or expose firms to a common condition, so its association is also left open and examined across participation intensity and transaction type.

Research Question 1 (RQ1): Relative to a single-link configuration, are open V-shaped and star configurations associated with different levels of corporate distance to default?

Hypothesis 4 (H4).

The presence of a closed 2 × 2 configuration and greater participation intensity in such configurations are associated with lower corporate distance to default.

Research Question 2 (RQ2): How are the presence and participation intensity of shared-counterparty bridges associated with corporate distance to default, and does the association vary across credit risk measures and transaction types?

3. Materials and Methods

3.1. Data Sources and Sample Construction

The initial dataset combines annual RPT disclosures, stock market information, financial statements, and corporate governance variables for Chinese A-share listed firms from CSMAR. The regression sample begins in 2003, when DD and the required market and financial variables become consistently available. Observations require a disclosed RPT amount and identifiable transaction parties. The 2006 Accounting Standard for Business Enterprises No. 36 and the 2021 revision of the listed-company disclosure measures are important reporting-regime landmarks [39,40]. We address long-horizon measurement comparability through year fixed effects, annual sample-flow diagnostics, later-period subsamples, period interactions, and within-year rank transformations, with the corresponding estimates reported in Appendix A 

Table A7. Alternative sample periods under the original firm-clustered specification.

Dimension	Variable	Merton DD		KMV DD
		2011–2024	2015–2024	2011–2024	2015–2024
Scale	Number of related parties	−0.0139	−0.0288 **	−0.051 ***	−0.060 ***
		(−1.056)	(−2.184)	(−3.058)	(−3.486)
	Total RPT amount	−0.0250 **	−0.0300 ***	−0.024 **	−0.027 ***
		(−2.268)	(−2.713)	(−2.473)	(−2.962)
	Average RPT amount	−0.0208 **	−0.0205 **	−0.010	−0.011
		(−2.110)	(−2.072)	(−1.192)	(−1.406)
Projected position	Projected degree centrality	−0.0048	−0.0092	−0.029	−0.044 **
		(−0.394)	(−0.751)	(−1.557)	(−2.410)
	Projected closeness centrality	0.0139 **	0.0051	−0.034 ***	−0.038 ***
		(2.041)	(0.874)	(−3.067)	(−3.783)
Concentration	HHI	0.0013	0.0130	0.000	0.002
		(0.160)	(1.581)	(0.032)	(0.216)
	Largest-related-party share	−0.0001	0.0119	−0.000	0.003
		(−0.017)	(1.529)	(−0.041)	(0.416)
	Top-three-related-party share	−0.0014	0.0131	0.033 ***	0.037 ***
		(−0.153)	(1.464)	(2.606)	(2.713)
	Dependence index	0.0015	0.0138 *	0.003	0.004
		(0.182)	(1.653)	(0.338)	(0.528)
Controls	Firm age	0.4767 ***	0.2005 **	0.4135 ***	0.5326 ***
		(4.928)	(2.032)	(2.624)	(3.173)
	Tobin’s Q	0.0601 ***	0.0756 ***	−0.0545 ***	−0.0305 ***
		(3.602)	(5.925)	(−3.756)	(−3.403)
	Book-to-market ratio	−0.0457 ***	0.0188	−0.2197 ***	−0.1460 ***
		(−2.807)	(1.166)	(−12.593)	(−8.528)
	Firm size (ln total assets)	−0.3721 ***	−0.3559 ***	−0.5509 ***	−0.5208 ***
		(−9.954)	(−9.168)	(−11.864)	(−9.604)
	Leverage	−0.1557 ***	−0.1803 ***	−0.1236 ***	−0.0889 ***
		(−6.293)	(−6.505)	(−7.271)	(−7.188)
	Cash holdings (ln)	0.1071 ***	0.1513 ***	0.1493 ***	0.1687 ***
		(5.538)	(7.583)	(7.330)	(8.355)
	ROA	−0.0212	−0.0466 ***	−0.0030	0.0075
		(−1.386)	(−4.830)	(−0.257)	(0.727)
Fixed effects	Fixed effects	Firm FE + year FE	Firm FE + year FE	Firm FE + year FE	Firm FE + year FE
Observations	Observations	20,387	16,658	20,387	16,658
Adjusted R2	Adjusted R2	0.5872	0.5747	0.6699	0.7033

Note: This table reports the original specification as a sensitivity check. Its lagged columns use the previous available firm observation rather than an exact adjacent calendar year, standard errors are clustered only by firm, and the original control vector excludes state ownership. The revised primary models use exact t − 1 timing for both network variables and controls, include state ownership, and cluster by firm and year. ***, **, and * denote significance at the 1%, 5%, and 10% levels.

and

Table A12. Period interaction and within-year rank tests of temporal stability.

Test/Network Measure	Outcome	Coefficient	t Statistic	p	N
Panel A: Period interaction estimates
Post-2011 × closed 2 × 2 presence	Merton DD	−0.0260	(−0.437)	0.6623	22,351
Post-2011 × projected degree	Merton DD	−0.0020	(−0.136)	0.8920	22,351
Post-2011 × closed 2 × 2 presence	KMV DD	−0.0819	(−0.924)	0.3557	22,351
Post-2011 × projected degree	KMV DD	−0.0337	(−1.248)	0.2120	22,351
Post-2015 × closed 2 × 2 presence	Merton DD	0.0270	(0.537)	0.5913	22,351
Post-2015 × projected degree	Merton DD	0.0072	(0.504)	0.6145	22,351
Post-2015 × closed 2 × 2 presence	KMV DD	−0.0174	(−0.211)	0.8329	22,351
Post-2015 × projected degree	KMV DD	−0.0272	(−0.993)	0.3208	22,351
Panel B: Within-year rank estimates
Related-party count	Merton DD	−0.0531 ***	(−4.219)	<0.001	22,351
Total RPT amount	Merton DD	−0.0593 ***	(−5.866)	<0.001	22,351
Average RPT amount	Merton DD	−0.0330 ***	(−3.539)	<0.001	22,351
HHI	Merton DD	0.0157 *	(1.714)	0.0866	22,351
Top-three share	Merton DD	0.0301 ***	(2.933)	0.0034	22,351
Projected degree	Merton DD	−0.0234 ***	(−2.824)	0.0047	22,351
Closed 2 × 2 intensity	Merton DD	−0.0303 ***	(−2.820)	0.0048	22,351
Related-party count	KMV DD	−0.0558 ***	(−3.604)	<0.001	22,351
Total RPT amount	KMV DD	−0.0309 **	(−2.063)	0.0392	22,351
Average RPT amount	KMV DD	−0.0157	(−1.259)	0.2081	22,351
HHI	KMV DD	0.0201 **	(2.425)	0.0153	22,351
Top-three share	KMV DD	0.0382 ***	(3.511)	<0.001	22,351
Projected degree	KMV DD	−0.0345 **	(−2.524)	0.0116	22,351
Closed 2 × 2 intensity	KMV DD	−0.0303 *	(−1.818)	0.0690	22,351

Note: Panel A reports the interaction term from separate exact t−1 models that include the focal network measure, lagged financial controls, firm and year fixed effects, and two-way firm-year clustered standard errors. Post-2011 and post-2015 refer to the lagged network year. Panel B replaces the focal measure with its standardized within-year percentile rank and otherwise retains the same exact-lag specification. Coefficients and t statistics are reported; N = 22,351 in every model. * p < 0.10, ** p < 0.05, *** p < 0.01.

.

Listed firms were keyed by stock code and year, and related-party names were standardized within each year before annual networks were constructed. The implementation applies Unicode NFKC normalization, converts strings to lower case, trims leading and trailing spaces, removes all remaining whitespace, and deletes common Chinese and English punctuation (middle dots, commas, periods, semicolons, colons, parentheses, and square brackets). Matching is exact on the resulting standardized string within year. Legal suffixes are retained to avoid merging distinct legal entities; abbreviations and alternate or historical names are not algorithmically expanded or fuzzily matched. These conservative rules prioritize precision, and the identifier-only sensitivity network provides complementary validation where source identifiers are available. The procedure is implemented in the replication file revision_work/raw_network_analyses.py (function clean_name). Network measures were matched to the regression data by stock code and year. Source counterparty IDs are available for a substantial subset of operation records and are used for a conservative sensitivity network. Among records with a non-missing identifier, 98.8–99.7% of distinct counterparty IDs are associated with one standardized disclosed name within a year, and 99.7–100.0% of distinct standardized names with an identifier correspond to one ID. These percentages assess within-year name-ID consistency rather than the prevalence of common counterparties across listed firms; they indicate limited name splitting and name-based entity conflation. The identifier-only network provides a direct entity resolution check, while the broader standardized-name network remains primary because it covers more disclosed relationships. A stratified manually coded benchmark linked to historical-name registries would permit formal precision and recall. The final sample contains 2674 firms and 26,264 firm-years over 2003–2024, all with at least one observed RPT link; the estimates are conditional on RPT-active firm-years. Requiring an exact adjacent calendar year for both network variables and controls yields 22,351 observations. Appendix A 

Table A3. Annual composition of the RPT-active regression sample.

Year	CSMAR Firms with an RPT Operation Record	Firms with at Least One Counterparty ID	Processed Network Firms (Reported Years)	Final Regression Firms	Final/Usable Raw-Record Network
2003	1085	964	n.a.	388	37.7%
2004	1289	1170	n.a.	391	31.2%
2005	1295	1190	1251	424	33.3%
2006	1364	1265	n.a.	421	31.5%
2007	1493	1354	n.a.	455	31.2%
2008	1567	1451	n.a.	580	37.8%
2009	1699	1567	n.a.	646	38.8%
2010	1997	1768	1697	715	37.1%
2011	2223	1928	n.a.	908	43.2%
2012	2298	2091	n.a.	1095	48.9%
2013	2355	2151	n.a.	1149	50.2%
2014	2616	2306	n.a.	1161	47.2%
2015	2820	2527	2265	1284	47.6%
2016	3114	2732	n.a.	1418	47.4%
2017	3491	3044	n.a.	1517	45.5%
2018	3586	3186	n.a.	1749	50.8%
2019	3801	3341	n.a.	1780	49.0%
2020	4251	3666	3509	1833	45.4%
2021	4760	4055	3880	1978	43.7%
2022	5134	4288	4204	2072	42.9%
2023	5365	4413	4413	2138	42.6%
2024	n.a.	n.a.	4505	2162	48.0%

Note: The operation-record stages are reconstructed directly for 2003–2023. For 2024, the table uses the complete updated processed-network count of 4505 and does not treat the available operation-record slice as a full-year denominator. The denominator in the last column is the annual raw-record network after requiring a named company counterparty, a positive CNY amount, and a direct listed-company RPT. Every final regression observation is RPT-active. Extending the flow to zero-RPT firms requires a consistently screened annual listed-firm universe, because the absence of an operation record cannot by itself distinguish zero activity from coverage or matching.

and

Table A4. Validation of the operation record network reconstruction.

Existing Measure	Operation-Record Reconstruction	N	Pearson	Spearman	Median Absolute Difference
Degree	Degree	22,338	0.989	0.950	1.000
Strength	Strength	22,338	1.000	0.918	476.704
Projected degree	Projected degree	22,338	0.385	0.779	0.000

Note: Operation records are restricted to direct listed-company RPTs, corporate counterparties, positive CNY amounts, and annual aggregation. This stricter record-level screen yields 22,338 exact-lag observations; the 13-observation difference from the 22,351 main sample consists of otherwise eligible firm-years whose eligible operation records after the remaining filters are denominated in USD. The reconstructed focal degree and total amount correlate 0.989 and 1.000 with the existing measures. Among records with a non-missing identifier in 2002–2023, 98.8–99.7% of distinct counterparty IDs are associated with one standardized disclosed name within a year, and 99.7–100.0% of distinct standardized names with an identifier correspond to one ID. These percentages assess name–ID consistency rather than the prevalence of common counterparties across listed firms. They support an identifier-only sensitivity test, while the broader name-standardized network remains primary because it covers more disclosed relationships.

report annual sample stages and reconstruction diagnostics.

The edge-level and direction-specific analyses contain 22,338 rather than 22,351 observations because their reconstruction additionally requires at least one direct, identifiable, positive-amount RPT denominated in CNY in the preceding network year. Thirteen otherwise eligible firm-years have no operation record satisfying this complete screen; after the remaining filters, their eligible operation records are denominated in USD. The difference therefore reflects the conservative operation-record currency screen used to construct the supplemental edge-level measures, rather than missing outcome or control variables.

Annual coverage expands sharply over the sample. Later-period subsamples, period interactions, and within-year rank transformations therefore provide complementary evidence on temporal stability (Appendix A Table A7 and Table A12). Scale remains broadly stable, the top-three-share result remains most visible in KMV DD, and projected position and configuration results vary more across outcomes and periods. For closed 2 × 2 presence and projected degree, the post-2011 and post-2015 interaction terms are statistically insignificant for both Merton and KMV DD, indicating no discrete common breakpoint at those dates. Within-year rank specifications preserve the main double-edged pattern: scale and projected degree are negatively associated with DD, the top-three share is positively associated with DD, and ranked closed intensity remains negative (statistically significant for Merton and marginal for KMV). These results complement the period-specific estimates and support a measured interpretation of temporal stability.

The unit of analysis is the listed firm-year. Multiple transactions between the same listed firm and related party in a year are aggregated into one weighted edge using total annual transaction amount. The primary network sums both directions because it measures the annual economic intensity of the relationship. Supplementary models use the source direction code to distinguish the listed company as seller/provider, buyer/recipient, or indeterminate; this role code is informative without assuming that every transaction implies an immediate cash inflow or outflow. The two partitions remain role-defined. A listed company disclosed as another firm’s related party is represented in the related-party role for that edge. Relationship codes identify parents, subsidiaries, entities under the same parent, and other disclosed categories; sensitivity tests remove the first three categories. Ultimate-controller links and legal creditor–debtor terms remain separate data requirements.

Continuous variables were winsorized at the 1st and 99th percentiles to limit the influence of extreme observations. Highly skewed amount and count variables were logarithmically transformed in accordance with their empirical definitions. The nine continuous network indicators and both DD measures were standardized before estimation. Accordingly, each coefficient represents the change in standardized DD associated with a one-standard-deviation increase in the corresponding network measure.

The contemporaneous specification relates year-t network characteristics and controls to year-t DD. The lagged specification requires an observed adjacent year and relates network characteristics and controls in t − 1 to DD in t. The previous-available-row implementation is retained only as a sensitivity check; 1239 of its 23,590 lagged observations span more than one calendar year.

3.2. Network Construction and Variable Measurement

Let $N\left(i,\mathrm{t}\right)$ denote the set of related parties connected to listed firm i in year t, and let $w_{ijt}$ denote the total transaction amount between firm i and related party j. The number of related parties, total RPT amount, and average RPT amount per related party are defined as follows:

$${\mathit{Degree}}_{it}=\left|N\left(i,\mathrm{t}\right)\right|$$

(1)

$${Strength}_{it}=\sum _{j\in N\left(i,t\right)}{w}_{ijt}$$

(2)

$${Avg\_txn}_{it}={\displaystyle \frac{{Strength}_{it}}{{\mathit{Degree}}_{it}}}$$

(3)

Define ${share}_{ijt}={\displaystyle \frac{w_{ijt}}{{Strength}_{it}}}$. HHI summarizes the full distribution of transaction shares, the largest-related-party share isolates the dominant relationship, the top-three-related-party share captures the combined importance of the three largest counterparties, and the dependence index applies nonlinear weights to the transaction shares:

$${HHI}_{it}=\sum _{j\in N\left(i,t\right)}{{share}_{ijt}}^2$$

(4)

$${Top1\_share}_{it}=\underset{j\in N\left(i,t\right)}{\mathit{max}}{share}_{ijt}$$

(5)

$${Top3\_share}_{it}=\sum _{j\in Top3\left(i,t\right)}{share}_{ijt}$$

(6)

$${Dependence\_index}_{it}=\sum _{j\in N\left(i,t\right)}{share}_{ijt}log(1+{share}_{ijt})$$

(7)

The interfirm projection is generated from each annual bipartite network. Two listed firms are connected when they share at least one related party. Projected degree centrality is the number of listed firms directly connected to the focal firm, divided by the maximum possible number of such connections. Projected closeness centrality is calculated using the Wasserman–Faust correction for disconnected networks, which combines the proportion of reachable firms with the average shortest-path distance to those firms [30].

The projection is used only to measure relative position among listed firms and is not treated as a complete substitute for the underlying bipartite network [41,42,43]. An unweighted one-mode projection does not preserve the number of shared related parties: a pair sharing one related party and a pair sharing several related parties are both represented by a single projected edge. Large related parties may also generate many projected connections. For this reason, local configurations are identified from the original bipartite network, where the number and arrangement of shared related parties remain observable. The projection captures interfirm reach, whereas the bipartite representation preserves the structure underlying those projected connections.

3.3. Identification of Local Network Microstructures

As shown in Figure 1, basic configurations are identified from the focal firm’s number of direct related parties. A single-link configuration connects the listed firm to one related party, an open V-shaped configuration connects it to two related parties, and a star configuration connects it to three or more related parties. Because the listed-firm related-party network is bipartite, nodes belonging to the same set are not directly connected. The three-node structure containing one listed firm and two related parties is not a closed triangle. The term open V-shaped configuration is used to distinguish this bipartite structure from triadic closure in a one-mode network.

Complex configurations are identified directly from the annual bipartite networks. A shared-counterparty bridge occurs when the focal listed firm and another listed firm are connected through a single common related party. The bridge count records the number of such local connections involving the focal firm. A closed 2 × 2 configuration occurs when two listed firms are each connected to at least two of the same related parties, creating a four-node locally closed structure. In graph-theoretic terms, the minimal closed 2 × 2 configuration is a bipartite K_2,2, commonly referred to as a butterfly. For each complex configuration, the existence indicator equals one when the firm participates in at least one such configuration during the year and zero otherwise. Participation intensity is measured as $ln(1+count)$, distinguishing entry into a local structure from the depth of participation. The main presence and participation intensity measures are constructed from the full annual RPT network. Transaction type-specific configurations are reconstructed only for the heterogeneity analysis.

3.4. Credit Risk Measures and Empirical Models

Corporate credit risk is measured using Merton DD and KMV DD [44,45,46]. Both measures express the distance between a firm’s estimated asset value and its default point in units of asset value volatility; higher values indicate a larger credit safety margin. The underlying structural model expression is

$$DD={\displaystyle \frac{\ln \left(\frac{V_A}{D}\right)+\left(\mu -0.5{\sigma }^2\right)T}{\sigma \sqrt{T}}}$$

(8)

where $V_A$ is the market value of assets, $D$ is the default boundary, $\mu$ is the expected asset return, $\sigma$ is asset volatility, and $T$ is the horizon, set to one year. Market equity value is calculated from the observed share price and total shares outstanding, equity volatility is estimated from stock returns, and the unobserved asset value and asset volatility are recovered iteratively. Merton DD provides the structural model benchmark, whereas KMV DD modifies the default point and empirical inputs. The robustness analysis employs the Bharath–Shumway simplified distance to default (BhSh DD) [47], the Altman Z-score [48], and a reverse-coded Ohlson O-score.

Each of the nine continuous network indicators is entered into a separate primary regression. This is deliberate: count, total amount, and average amount are algebraically linked, while the four concentration measures summarize overlapping transaction–share distributions. Saturated VIFs are consequently very large, whereas a parsimonious model containing count, total amount, HHI, and projected degree has VIFs from 1.18 to 2.72. Appendix A 

Table A2. Variance inflation diagnostics.

Specification Family	Minimum VIF	Maximum VIF	Indicators
All nine network indicators	1.74	2653.78	9
Parsimonious joint total	1.18	2.72	4
Saturated scale joint	1.21	769.09	5
Four concentration measures	22.69	2639.10	4

Note: The nine-indicator and saturated scale models exhibit severe multicollinearity because count, total amount, average amount, and several concentration measures are algebraically or conceptually overlapping. The parsimonious count-total HHI-projected-degree model has VIFs from 1.18 to 2.72. The primary table therefore estimates the nine indicators separately and uses parsimonious joint models as diagnostics.

reports the diagnostics, and joint models are used as robustness checks rather than replacements for the interpretable single-indicator estimates.

The firm-level controls are firm age, Tobin’s Q, the book-to-market ratio, the logarithm of total assets, leverage, the logarithm of cash holdings, return on assets (ROA), and state ownership. Variable definitions, additional regression results and the reported control-variable blocks are presented in Appendix A. Where representative control coefficients are reported to conserve space, this is stated in the corresponding table notes.

Data processing, network construction, and statistical analyses were conducted primarily in Python (version 3.9.12). All revised primary models include firm and year fixed effects, state ownership, and two-way firm-year clustered standard errors, thereby addressing within-firm serial dependence and common annual dependence. Source relationship codes support exclusions of parents, subsidiaries, and entities under the same parent. Holm family-wise and Benjamini–Hochberg false-discovery adjustments are reported for the primary families and targeted edge-level robustness families. Coefficients are interpreted as conditional within-firm associations, consistent with the study’s objective of identifying firm-level relational risk signals.

$${DD}_{i,t}=\alpha +\beta {\mathit{Network}}_{i,t-k}+\gamma {Controls}_{i,t-k}+{\mu }_i+{\lambda }_t+{\epsilon }_{i,t}$$

(9)

$${DD}_{i,t}{\mathit{Network}}_{i,t-k}{Controls}_{i,t-k}{\mu }_i{\lambda }_t$$

The dependent variable is the DD of firm i in year t. The focal network measure and the control vector are both measured in t − k, with k = 0 for the contemporaneous model and k = 1 for the exact adjacent-year model. For closed configurations, supplementary models progressively add focal degree, total or average RPT amount, concentration, and projected degree; coarsened degree-volume reweighting and opportunity-residualized closure provide additional benchmarks. Holdout prediction uses a rolling-origin design over 2018–2024: for each test year y, ridge models are re-estimated using only observations dated through y − 1 and then predict year y on a common complete sample. This annual updating rule preserves temporal ordering and avoids making the result depend on a single training cutoff.

$${DD}_{i,t}=\alpha +{\sum }_m{\beta }_m{Micro}_{m,i,t-\mathrm{k}}+\gamma {Controls}_{i,t-\mathrm{k}}+{\mu }_{\mathrm{i}}{+{\lambda }_t+\epsilon }_{i,t}$$

(10)

Three mechanism variables are used. Related-party fund occupation is related-party other receivables divided by total assets. The resource coordination index is the equal-weighted mean of standardized gross margin, total-asset turnover, accounts-receivable turnover, inventory turnover, and the reverse-signed management-expense ratio. Gross margin equals (operating revenue − operating cost) divided by operating revenue. Total-asset turnover and accounts-receivable turnover equal operating revenue divided by average total assets and average accounts receivable, respectively. Inventory turnover equals operating cost divided by average inventory, and the management expense ratio equals management expenses divided by operating revenue. Within-configuration transaction intensity is the natural logarithm of the transaction amount carried by the relevant local configuration.

The channel analysis reports two conditional regressions and the product of their coefficients. These estimates are used as descriptive channel correlations because the network variable and proposed channel may share accounting inputs or transaction construction. They organize economically plausible links involving fund occupation, resource coordination, and transaction intensity and provide a clear basis for future designs with separately timed channel measures.

4. Results

4.1. Evolution and Structural Properties of the RPT Network

Before estimating the firm-level models, Figure 2 and Figure 3 describe the evolution of the RPT system. Figure 2 summarizes changes in network scale and density, while Figure 3 visualizes selected projected interfirm connections created by shared related parties. They provide system-level context for the firm-level regressions.

Figure 2 and

Table 1. RPT network statistics for representative years.

Year	Total Nodes	Listed Firms	Related-Party Nodes	Transaction Links	Mean Listed-Firm Degree	Density
2000	5958	933	5025	5091	5.46	0.001086
2005	10,378	1251	9127	9363	7.48	0.000820
2010	13,778	1697	12,081	12,853	7.57	0.000627
2015	22,743	2265	20,478	22,171	9.79	0.000478
2020	46,412	3509	42,903	47,953	13.67	0.000319
2024	59,225	4505	54,720	63,122	14.01	0.000256

Note: Listed firms are the focal nodes disclosing RPTs. Related-party nodes include controlling shareholders, subsidiaries, associates, and other transaction counterparties. Transaction links are edges in the annual bipartite network.

document the substantial expansion of the RPT network. Total nodes rose from 5958 in 2000 to 59,225 in 2024, listed-firm nodes from 933 to 4505, and transaction links from 5091 to 63,122. Mean degree among listed firms increased from 5.46 to 14.01. By 2024, the average listed firm was connected to 14.01 related parties, compared with 5.46 in 2000.

Expansion did not generate uniform connectivity. Network density declined from 0.001086 to 0.000256 because the number of possible listed-firm–related-party pairs grew faster than the number of observed transaction links. New relationships remained concentrated in particular firms and local units. Figure 3 further shows that the projected network became larger and more internally differentiated over time. By 2024, the network was larger and more locally differentiated but remained globally sparse.

These descriptive patterns motivate the measures used below. Node and link growth is captured by firm-level scale and transaction intensity variables; connections through shared counterparties are captured by projected centrality; and local sharing is represented by bridge and closed 2 × 2 configurations.

4.2. Descriptive Statistics

Table 2. Descriptive statistics.

Variable	N	Mean	SD	Min.	Median	Max.
Merton DD	26,264	7.071	3.170	2.158	6.396	17.807
KMV DD	26,264	0.919	1.913	−9.706	1.323	3.635
Number of related parties	26,264	11.163	19.371	1	6	701
Total RPT amount (CNY 10,000)	26,264	450,264	30,300,000	0.001	35,835	4.91 × 109
Average RPT amount (CNY 10,000)	26,264	33,719	2,020,000	0.001	5773	3.27 × 108
HHI	26,264	0.552	0.282	0.010	0.501	1
Largest-related-party share	26,264	0.655	0.248	0.030	0.643	1
Top-three-related-party share	26,264	0.900	0.144	0.074	0.973	1
Dependence index	26,264	0.415	0.182	0.010	0.399	0.693
Projected degree centrality	26,264	0.000262	0.000674	0	0	0.008
Projected closeness centrality	26,264	0.000611	0.002	0	0	0.023
Single link	26,264	0.0200	0.1401	0	0	1
Open V-shaped configuration	26,264	0.0551	0.2282	0	0	1
Star configuration	26,264	0.9249	0.2636	0	1	1
Shared-counterparty bridge: presence	26,264	0.1717	0.3771	0	0	1
Closed 2 × 2: presence	26,264	0.1156	0.3198	0	0	1
Shared-counterparty bridge: intensity	26,264	0.1353	0.3092	0	0	2.0794
Closed 2 × 2: intensity	26,264	0.2796	0.9466	0	0	8.2287

Note: Merton DD and KMV DD are shown before standardization; the regressions use standardized measures. Amount variables are strongly right-skewed and are transformed and standardized following the original specification.

summarizes the distribution of the credit risk measures, the nine continuous network indicators, and the local configuration variables. The variables are discussed in the same order as the empirical analysis (DD and continuous network characteristics first, followed by local configurations).

The two DD measures display substantial cross-sectional and time-series variation. Before standardization, Merton DD has a mean of 7.071 and a standard deviation of 3.170, while KMV DD has a mean of 0.919 and a standard deviation of 1.913. Both measures vary substantially across firm-years.

The network variables are also highly dispersed. The mean firm-year has 11.163 related parties, but the median is only 6 and the maximum is 701. Transaction amounts are similarly right-skewed. Concentration is generally high: mean HHI is 0.552, the largest related party accounts for 65.5% of RPT value on average, and the top three account for 90.0%. Projected degree and closeness centrality are close to zero for most observations, indicating that many firms remain peripheral even though a smaller group occupies substantially more connected positions.

Stars account for 92.49% of firm-year observations, whereas single links and open V-shaped configurations account for 2.00% and 5.51%, respectively. Because stars account for more than 90% of observations, this category groups together firms with three to several hundred related parties. Complex configurations add further variation: 17.17% of observations contain a shared-counterparty bridge and 11.56% contain a closed 2 × 2 configuration, with highly right-skewed participation intensities. This imbalance makes continuous-scale measures useful alongside, but analytically distinct from, complex local configurations.

4.3. Network Scale, Transaction Concentration, and Projected Position

Table 3. RPT network characteristics and corporate credit risk.

Measure		Merton DD		KMV DD
		${\mathbf{R}\mathbf{P}\mathbf{T}}_{\mathbf{t}}$	${\mathbf{R}\mathbf{P}\mathbf{T}}_{\mathbf{t}-1}$	${\mathbf{R}\mathbf{P}\mathbf{T}}_{\mathbf{t}}$	${\mathbf{R}\mathbf{P}\mathbf{T}}_{\mathbf{t}-1}$
Network scale	Number of related parties	−0.053 ***	−0.054 ***	−0.088 ***	−0.090 ***
		(−3.770)	(−3.991)	(−4.800)	(−4.254)
	Total RPT amount	−0.045 ***	−0.051 ***	−0.043 ***	−0.048 ***
		(−3.966)	(−4.770)	(−3.252)	(−3.499)
	Average RPT amount	−0.027 ***	−0.032 ***	−0.016	−0.018 *
		(−2.989)	(−3.207)	(−1.541)	(−1.773)
Projected position	Projected degree centrality	−0.023 **	−0.023 **	−0.025 *	−0.025
		(−2.459)	(−2.475)	(−1.814)	(−1.564)
	Projected closeness centrality	0.000	−0.000	−0.041 **	−0.046 *
		(0.044)	(−0.036)	(−2.323)	(−1.850)
Concentration	HHI	0.014	0.014	0.018 **	0.017 **
		(1.256)	(1.527)	(2.062)	(2.188)
	Largest-related-party share	0.013	0.012	0.021 **	0.018 **
		(1.223)	(1.391)	(2.370)	(2.219)
	Top-three-related-party share	0.014	0.015	0.060 ***	0.063 ***
		(1.425)	(1.439)	(4.023)	(4.432)
	Dependence index	0.015	0.015	0.022 **	0.022 ***
		(1.298)	(1.589)	(2.373)	(2.584)
Observations		26,264	22,351	26,264	22,351

Note: Each of the nine network variables enters a separate regression. Current specifications use year-t network variables and controls; lagged specifications require an exact adjacent calendar year and use both network variables and controls at t − 1. All revised models include the controls in Appendix A Table A1 (including state ownership), firm and year fixed effects, and two-way firm-year clustered standard errors. t-statistics are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% levels. Higher DD indicates lower credit risk.

reports the revised separate-indicator estimates. Current models use current controls; exact t − 1 models use exact t − 1 controls. All specifications include firm and year fixed effects and use firm-year two-way clustered standard errors. Appendix A Table A2 and

Table A9. Multiple-inference adjustments for selected findings.

Measure	Merton p	Merton BH q	Merton Holm	KMV p	KMV BH q	KMV Holm
Related-party count	0.0001	0.0003	0.0010	0.0000	0.0001	0.0003
Total RPT amount	0.0000	0.0000	0.0000	0.0005	0.0017	0.0065
Average RPT amount	0.0013	0.0040	0.0175	0.0763	0.1144	0.5339
Top-three share	0.1500	0.1688	0.6728	0.0000	0.0001	0.0002
Projected degree	0.0133	0.0300	0.1466	0.1179	0.1515	0.6728
Closed 2 × 2 presence	0.0060	0.0242	0.0434	0.0712	0.1898	0.4270
Closed 2 × 2 intensity	0.0054	0.0242	0.0434	0.1186	0.2149	0.5930

Note: Corrections are applied within the 18 continuous-indicator tests and within the 8 complex-configuration tests. The Merton closed-configuration presence and intensity results retain BH q = 0.024 and Holm-adjusted p = 0.043; they nevertheless attenuate in the saturated joint model in Appendix Table A17.

report multicollinearity and multiple-inference diagnostics.

The three scale measures yield the most stable continuous-variable pattern. In the exact t − 1 models, related-party count is negatively associated with Merton DD (coefficient −0.0542, p < 0.001) and KMV DD (−0.0905, p < 0.001); total amount is also negative for both outcomes (−0.0514 and −0.0481), and average amount remains negative for Merton DD (−0.0316, p = 0.001). These scale results survive both Holm and Benjamini–Hochberg adjustments.

Count, total amount, and average amount provide complementary summaries of relationship breadth, aggregate resource commitment, and the financial importance of a typical tie. Their common negative sign indicates that as the RPT system around a firm becomes broader or more financially intensive, the associated coordination, settlement, monitoring, and counterparty-exposure burden coincides with a smaller credit buffer after conventional financial controls and fixed effects are held constant.

Concentration provides the stabilizing side of the firm-level pattern. The top-three share is positively associated with KMV DD in the exact t − 1 model (0.0632, p < 0.001; BH q < 0.001) and is the primary concentration finding. HHI, the largest-party share, and the dependence index are also positive at conventional unadjusted levels, although HHI and the largest-party share are marginal after false-discovery adjustment; the Merton estimates are comparatively small. Economically, the KMV result is consistent with repeated exchange among a focused set of core related parties improving information, resource matching, and the predictability of internal coordination. Counterparty quality, substitutability, and governance determine whether these coordination benefits outweigh concentration-related dependence.

Projected degree is negatively associated with Merton DD in the separate exact-lag model (−0.0234, p = 0.013; BH q = 0.030) and attenuates when focal breadth and closure enter jointly. A firm connected to more listed companies through shared related parties may gain information and resources while also facing a wider set of common transaction environments and more complex monitoring and responsibility allocation. Edge-level sensitivity tests add counterparty average and maximum degree, remove the top 1% of counterparty hubs, construct an inverse popularity-weighted projection, and rebuild projected degree from source IDs. After popularity controls, reconstructed projected degree is negative for KMV DD (−0.1622, p = 0.024), the identifier-only coefficient is also negative (−0.1560, p = 0.011), and hub-downweighted projection is negative for BhSh DD (−0.0471, p = 0.038). Their shared direction indicates that projected reach carries information beyond the presence of a small number of popular counterparties, with strength that varies across DD measures.

Viewed jointly, the three classes of firm-level RPT indicators display a double-edged association with corporate credit risk. Greater relationship scale and wider projected reach are associated with thinner credit buffers, indicating that exposure, coordination, and monitoring costs can outweigh the resource-access benefits of relational expansion. By contrast, the positive KMV association of the top-three share shows how concentrating transactions among a manageable set of core counterparties can improve continuity and information quality. The comparison distinguishes the expansion of relationships from the allocation of value across existing relationships and shows how coordination benefits and dependence costs vary across network dimensions and DD measures.

Table 4. Economic magnitude of selected KMV estimates.

Measure	Contrast	Change in Raw KMV DD	Approximate Change in Implied PD (bp)
Related-party count	P25 to P75	−0.230	443.6
Total RPT amount	P25 to P75	−0.106	189.9
Top-three share	P25 to P75	0.137	−207.3
Projected degree	P50 to P90 (IQR is zero)	−0.064	111.3
Closed 2 × 2 presence	0 to 1	−0.173	322.4

Note: DD is the number of asset-volatility units separating asset value from the default point; a negative change therefore indicates a thinner structural credit buffer. Probability translations apply the standard normal CDF to the median KMV DD and are model-based illustrations rather than observed default frequencies or causal effects. The closed-configuration magnitude is reported as a separate-model contrast, with the corresponding joint-specification evidence presented in Appendix A Table A17.

translates selected KMV estimates into the units of the structural credit buffer. DD records the number of asset-volatility units separating asset value from the default point, so a decline represents a thinner cushion. Moving related-party count from the 25th to the 75th percentile is associated with an approximate 0.230 decline in raw KMV DD and an illustrative 443.6-basis-point increase in normal-model implied default probability at the sample median. The corresponding total amount contrast reduces DD by 0.106 and raises implied probability by 189.9 basis points. By contrast, an interquartile increase in the top-three share raises KMV DD by about 0.137 and lowers implied probability by 207.3 basis points. These contrasts give the double-edged result direct economic meaning: relational expansion is associated with a thinner estimated credit buffer, whereas focused allocation among three core counterparties is associated with a larger KMV buffer. The probability translations provide a common scale for interpreting the structural estimates.

4.4. Local Network Microstructures and Credit Risk

Table 3 identifies distinct relationships between DD and relational breadth, transaction value, concentration, and projected position. These measures do not, however, retain the full local organization of the underlying ties. A projected edge records whether two listed firms share at least one related party, so a connection supported by one shared party is represented in the same way as a connection supported by several. Similarly, the number of related parties cannot distinguish an ordinary star from a star containing nodes shared with other listed firms.

The local configuration analysis restores information lost through projection and annual aggregation. Basic configurations test whether broad counterparty-count categories produce meaningful group differences. A shared-counterparty bridge identifies a local connection supported by one common node, whereas a closed 2 × 2 configuration captures repeated sharing and cross-closure.

Table 5. Local RPT network microstructures and corporate credit risk.

	Current Microstructures			Exact t − 1 Microstructures
	(1) Basic	(2) Presence	(3) Intensity	(1) Basic	(2) Presence	(3) Intensity
Panel A: ${\mathbf{M}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{o}\mathbf{n}\_\mathbf{D}\mathbf{D}}_{\mathbf{t}}$
Open V-shaped configuration	−0.0293	−0.0298	−0.0296	−0.0081	−0.0079	−0.0074
	(−0.507)	(−0.519)	(−0.515)	(−0.155)	(−0.153)	(−0.144)
Star configuration	−0.0853	−0.0864 *	−0.0878 *	−0.0508	−0.0512	−0.0524
	(−1.619)	(−1.647)	(−1.682)	(−0.989)	(−0.997)	(−1.024)
Bridge presence		0.0049			−0.0140
		(0.233)			(−0.896)
Closed 2 × 2: presence		−0.0950 ***			−0.0919 ***
		(−3.044)			(−2.746)
Bridge intensity			0.0117			−0.0088
			(0.475)			(−0.421)
Closed 2 × 2: intensity			−0.0390 ***			−0.0338 ***
			(−3.675)			(−2.781)
Observations	26,264	26,264	26,264	22,351	22,351	22,351
Panel B: ${\mathbf{K}\mathbf{M}\mathbf{V}\_\mathbf{D}\mathbf{D}}_{\mathbf{t}}$
Open V-shaped configuration	−0.0406	−0.0416	−0.0418	0.0014	0.0016	0.0020
	(−1.149)	(−1.198)	(−1.216)	(0.040)	(0.045)	(0.058)
Star configuration	−0.0374	−0.0377	−0.0390	0.0002	0.0000	−0.0007
	(−0.915)	(−0.941)	(−0.991)	(0.006)	(0.000)	(−0.017)
Bridge presence		−0.0405			−0.0173
		(−1.581)			(−0.677)
Closed 2 × 2: presence		−0.1109 **			−0.0906 *
		(−2.273)			(−1.805)
Bridge intensity			−0.0872 **			−0.0564
			(−2.501)			(−1.497)
Closed 2 × 2: intensity			−0.0379 *			−0.0375
			(−1.845)			(−1.561)
Observations	26,264	26,264	26,264	22,351	22,351	22,351

Note: Current specifications use year-t network variables and controls; lagged specifications require an exact adjacent calendar year and use both network variables and controls at t − 1. All revised models include the controls in Appendix A Table A1 (including state ownership), firm and year fixed effects, and two-way firm-year clustered standard errors. t-statistics are in parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% levels.

examines the associations between these local arrangements and DD, complementing the continuous-characteristic and economic-magnitude results in Table 3 and Table 4.

The open-V and star categories provide useful degree-based benchmarks, but they offer limited discrimination in the full sample. Stars account for 92.49% of firm-years and combine firms with very different continuous degrees, amounts, and shared-party opportunities. Continuous controls and the degree-volume comparisons in Appendix A 

Table A8. Correlations between local configurations and continuous network characteristics.

Configuration Measure	Degree	Total Amount	Average Amount	HHI	Top-Three Share	Projected Degree
bridge_shared_dummy	0.261	0.170	0.080	−0.150	−0.183	0.463
closed_2×2_dummy	0.432	0.247	0.093	−0.211	−0.272	0.621
ln1p_bridge_shared_cnt	0.290	0.188	0.088	−0.163	−0.210	0.508
ln1p_closed_2×2_cnt	0.458	0.238	0.072	−0.203	−0.286	0.590

Note: Pearson correlations are reported. Closed 2 × 2 presence correlates 0.432 with focal-firm degree and 0.621 with projected degree; the corresponding intensity correlations are 0.458 and 0.590. These values motivate the joint and opportunity-adjusted specifications.

and

Table A17. Progressive adjustment of the closed 2 × 2 coefficient.

Adjustment	Merton Presence	Merton Intensity	KMV Presence	KMV Intensity	BhSh Presence	BhSh Intensity
M0 configuration only	−0.0916 *** (−2.737)	−0.0334 *** (−2.746)	−0.0906 * (−1.803)	−0.0374 (−1.556)	−0.0849 *** (−3.008)	−0.0420 *** (−3.519)
M1 plus focal degree	−0.0667 ** (−1.988)	−0.0225 * (−1.894)	−0.0457 (−0.967)	−0.0184 (−0.785)	−0.0696 ** (−2.364)	−0.0363 *** (−3.047)
M2 plus total RPT	−0.0689 ** (−2.047)	−0.0241 ** (−2.021)	−0.0467 (−0.988)	−0.0191 (−0.814)	−0.0699 ** (−2.370)	−0.0365 *** (−3.110)
M3 plus concentration	−0.0679 ** (−2.046)	−0.0237 ** (−2.032)	−0.0415 (−0.884)	−0.0163 (−0.703)	−0.0664 ** (−2.271)	−0.0349 *** (−3.115)
M4 plus projected degree	−0.0550 (−1.425)	−0.0175 (−1.420)	−0.0312 (−0.570)	−0.0165 (−0.636)	−0.0685 * (−1.884)	−0.0359 *** (−2.860)

Note: Exact adjacent-year network variables and controls are used. All models include firm and year fixed effects and two-way firm-year clustered standard errors. The Merton coefficient remains significant after focal degree, total RPT amount, and HHI are added but attenuates after projected degree is included. BhSh intensity remains negative in the full joint specification. ***, **, and * denote significance at the 1%, 5%, and 10% levels.

therefore provide the more informative tests of relationship breadth and formation opportunities.

Closed 2 × 2 presence and intensity are negatively associated with Merton DD in the exact t − 1 primary models (−0.0919, p = 0.006; and −0.0338, p = 0.005), and both survive Benjamini–Hochberg and Holm correction within the complex-configuration family. Progressive controls show overlap with projected reach. The edge-level benchmarks then isolate an additional component. Observed closure exceeds the mean of 100 degree-sequence-preserving randomizations in every annual graph. Excess closure remains negatively associated with Merton DD (−0.0276, p = 0.019) and BhSh DD (−0.0336, p = 0.013) after focal degree, transaction amount, projected degree, and counterparty average and maximum degree are controlled; both survive BH and Holm adjustment within the three-outcome randomization family. Closed presence is also negative for Merton after popularity controls, and closed presence excluding parent, subsidiary, and same-parent edges is negative for KMV and survives Holm adjustment within the supplementary closure family. These results show that repeated local sharing contains information beyond the degree sequence while remaining complementary to projected position.

Bridge coefficients are comparatively outcome-dependent after the revised timing and inference choices and are treated as secondary evidence. This contrast with the stable scale pattern highlights the value of separating single shared-counterparty connections from repeated closed sharing.

Appendix A Table A8,

Table A10. Counterparty popularity, hub, and identifier sensitivity tests for projected position.

Supplementary Network Measure	Merton DD	KMV DD	BhSh DD
Projected degree + popularity controls	0.0113 (0.386)	−0.1622 ** (−2.256)	−0.0007 (−0.022)
Hub-downweighted projected strength	−0.0286 * (−1.700)	−0.0458 (−1.317)	−0.0471 ** (−2.076)
Projection after top-1% party hubs removed	−0.0027 (−0.218)	−0.0346 * (−1.710)	−0.0111 (−0.837)
Identifier-only projected degree	−0.0048 (−0.168)	−0.1560 ** (−2.532)	−0.0248 (−0.841)

Note: Popularity-conditioned models include focal degree, transaction amount, counterparty average and maximum degree, and closure. Hub-downweighted projection allocates each shared-party contribution inversely to its number of alternative listed-firm connections. The top-hub test removes related-party nodes in the top 1% of the annual counterparty-degree distribution, and the identifier-only model retains counterparties with a source ID. The consistently negative direction across these constructions shows that projected reach is not attributable solely to a few high-degree counterparties; the outcome dependence and multiple-inference results support treating this evidence as supplementary. **, and * denote significance at the 5%, and 10% levels.

, Table A17,

Table A18. Counterparty popularity, identifier, and intragroup sensitivity tests for closed 2 × 2 configurations.

Supplementary Network Measure	Merton DD	KMV DD	BhSh DD
Closed presence + popularity controls	−0.0553 ** (−2.077)	−0.0432 (−1.117)	−0.0261 (−0.927)
Closed presence excluding obvious intragroup edges	−0.0477 (−1.031)	−0.2500 *** (−3.002)	−0.0262 (−0.588)
Closed intensity excluding obvious intragroup edges	−0.0017 (−0.167)	−0.0458 ** (−2.424)	0.0036 (0.408)
Identifier-only closed intensity	−0.0139 (−1.139)	−0.0122 (−0.522)	−0.0281 ** (−2.011)

Note: Popularity-conditioned closure models include focal degree, transaction amount, counterparty average and maximum degree, and projected degree. Obvious intragroup edges are those involving a parent, subsidiary, or entity under the same parent (relationship codes 01–03). Identifier-only models retain counterparties with a source ID. The negative KMV closed-presence coefficient after obvious intragroup edges are removed survives Holm correction within the 18 supplementary closure tests (adjusted p = 0.048). Identifier-only coefficients are directionally consistent, with BhSh closed intensity being significant at the conventional level. *** and ** denote significance at the 1% and 5% levels.

and

Table A19. Degree-sequence-preserving bipartite randomization benchmarks.

Network Year	Edges	Regression-Sample Focal Firms	Observed Focal Closure	Mean Randomized Closure	Observed/Random
2002	5874	371	69	0.04	1725.0
2005	8682	409	293	0.58	505.2
2010	16,983	868	3621	2.84	1275.0
2015	33,620	1374	13,974	11.50	1215.1
2020	65,339	1943	50,239	123.33	407.4
2023	80,151	2128	161,429	219.67	734.9

Note: Each annual bipartite graph is randomized 100 times by valid double-edge swaps, preserving every listed-firm degree and every related-party degree exactly while preventing duplicate edges. Selected years are displayed; the comparison is conducted for every network year from 2002 through 2023. Observed closure exceeds the randomized mean for every year. The annual excess measure is log(1 + observed focal closure) minus log(1 + the focal firm’s randomized mean).

assess mechanical formation opportunities, while

Table 6. Credit risk regressions using excess closure relative to degree-preserving randomizations.

Outcome	Coefficient	t Statistic	p	BH q	Holm p	N
Merton DD	−0.0276 **	(−2.339)	0.0193	0.0290	0.0397	22,338
KMV DD	−0.0055	(−0.250)	0.8027	0.8027	0.8027	22,338
BhSh DD	−0.0336 **	(−2.478)	0.0132	0.0290	0.0397	22,338

Note: Exact t − 1 models control for focal degree, total RPT amount, projected degree, counterparty average and maximum degree, lagged financial controls, firm and year fixed effects, and two-way firm-year clustering. Excess closure is negatively associated with Merton and BhSh DD; both results retain BH q = 0.029 and Holm-adjusted p = 0.040 within the three-outcome randomization family. The estimates identify a local closure component above the bipartite degree sequence and aggregate transaction scale. ** denotes significance at the 5% levels.

reports the main excess-closure regressions immediately after the baseline microstructure evidence. Closed 2 × 2 presence correlates 0.432 with focal degree and 0.621 with projected degree; intensity correlations are 0.458 and 0.590. Merton closure remains negative after focal degree, total RPT amount, and HHI are added and becomes smaller once projected degree enters. The edge-level tests then condition on counterparty average and maximum degree, remove top hubs, use source IDs, exclude obvious parent–subsidiary and same-parent edges, and compare each observed annual graph with 100 degree-sequence-preserving randomizations. Excess closure remains negative for Merton and BhSh DD and survives BH and Holm correction across the three outcomes. The complete evidence distinguishes repeated closure from both simple breadth and a single shared-counterparty bridge: degree-based categories provide less discrimination, bridge estimates vary by outcome, and repeated sharing remains associated with a thinner asset-value buffer above the formation opportunities implied by both sides of the degree sequence. This pattern is consistent with common exposure, synchronized liquidity demands, monitoring complexity, and responsibility ambiguity outweighing the potential verification and coordination benefits of local closure in these specifications.

4.5. Robustness, Transaction Direction, and Transaction-Type Heterogeneity

Table 7. Robustness of complex-configuration results to alternative DD measures.

Variable	Merton/Current	KMV/Current	BhSh/Current	Merton/Exact t − 1	KMV/Exact t − 1	BhSh/Exact t − 1
Closed 2 × 2: presence	−0.0950 ***	−0.1109 **	−0.0913 ***	−0.0919 ***	−0.0906 *	−0.0847 ***
Closed 2 × 2: intensity	−0.0390 ***	−0.0379 *	−0.0439 ***	−0.0338 ***	−0.0375	−0.0418 ***
Shared-counterparty bridge: presence	0.0049	−0.0405	0.0060	−0.0140	−0.0173	−0.0225
Shared-counterparty bridge: intensity	0.0117	−0.0872 **	0.0155	−0.0088	−0.0564	−0.0204

Note: Each cell reports the coefficient on the focal variable. All credit risk measures are coded so that a higher value indicates lower risk. Other specifications follow the baseline local-configuration models in Table 5. ***, **, and * denote significance at the 1%, 5%, and 10% levels.

compares revised configuration estimates across Merton, KMV, and Bharath-Shumway DD. The negative closed-configuration coefficients are visible across the three structural outcomes and are strongest for Merton and BhSh DD. Appendix A Table A4, Table A17, Table A18 and Table A19 then add raw-source reconstruction, progressive controls, counterparty popularity tests, identifier-only and intragroup exclusion networks, and the annual degree-sequence-preserving randomization benchmark.

The closed-configuration coefficients are negative for all three structural DD measures in the separate exact-lag models and are strongest for Merton and BhSh DD. In the full joint specification, BhSh intensity remains negative and significant, while Merton presence and intensity attenuate, and the KMV estimates are less precise. The evidence therefore supports a consistent negative direction, with the clearest robustness for Merton and BhSh outcomes.

Altman Z-score and the reverse-coded O-score provide accounting-based comparisons with the structural DD measures. Because they rely primarily on accounting information—and the reverse O-score overlaps substantially with leverage and profitability controls—their response to local relationship changes differs from the market-based DD measures. Merton, KMV, and BhSh DD therefore provide the most directly comparable robustness family, while the accounting scores broaden the outcome perspective.

Alternative-outcome, sample-period, period interaction, and within-year-rank tests (Appendix A Table A7 and Table A12) sharpen the scope of the main conclusions. Scale coefficients remain the most stable, concentration is most visible in KMV and especially the top-three share, and projected position varies more by period and joint specification. This hierarchy clarifies which network dimensions provide broad evidence and which offer more outcome- or period-specific information.

Appendix A 

Table A11. Holdout predictive performance.

Outcome	Controls-Only RMSE	Full-Network RMSE	RMSE Change	Out-of-Sample R2	Test N
Merton DD	0.8445	0.8412	−0.394%	0.025	12,291
KMV DD	0.8552	0.8493	−0.692%	0.320	12,291
BhSh DD	0.8772	0.8720	−0.592%	−0.299	12,291

Note: Ridge models use a rolling-origin evaluation over 2018–2024. For each test year y, both the control benchmark and the full-network model are re-estimated using only common-complete observations dated through y − 1, and annual errors are pooled across the same 12,291 test observations. Adding the full network block reduces RMSE by approximately 0.39% for Merton, 0.69% for KMV, and 0.59% for BhSh; MAE also declines for all three outcomes. The reductions in RMSE and MAE are small. Out-of-sample R² is positive for Merton (0.025) and KMV (0.320) but negative for BhSh (−0.299). The exercise therefore provides modest supporting evidence rather than a uniform predictive gain across outcomes.

reports a rolling-origin holdout exercise over 2018–2024. Re-estimating both models before each test year and adding the network block to a demanding lagged financial control benchmark reduces pooled RMSE by 0.39% for Merton, 0.69% for KMV, and 0.59% for BhSh; pooled MAE declines by 0.31%, 0.86%, and 0.93%, respectively. These error reductions are small, and the out-of-sample R² is positive for Merton (0.025) and KMV (0.320) but negative for BhSh (−0.299). The exercise therefore provides modest supporting evidence that the network block adds predictive information, while also showing that the gain is not uniform across outcomes; prediction is treated as supplementary rather than primary evidence.

Table 8. Direction-specific RPT scale, concentration, projected position, and distance to default.

Direction-Specific Measure	Merton DD	KMV DD	BhSh DD
Seller/provider transaction amount	−0.0259 *** (−3.235)	−0.0276 *** (−2.975)	−0.0078 (−0.851)
Buyer/recipient transaction amount	−0.0410 *** (−3.982)	−0.0237 ** (−2.317)	−0.0168 * (−1.759)
Seller/provider relationship count	−0.0295 ** (−2.413)	−0.0653 *** (−4.353)	−0.0137 (−1.284)
Buyer/recipient relationship count	−0.0432 *** (−4.859)	−0.0399 *** (−2.597)	−0.0329 *** (−4.077)
Seller/provider HHI	0.0208 *** (2.648)	0.0136 (1.478)	0.0142 * (1.934)
Buyer/recipient HHI	0.0237 *** (4.149)	0.0298 *** (3.260)	0.0103 ** (1.991)
Seller/provider top-one share	0.0191 *** (2.635)	0.0149 * (1.650)	0.0140 ** (2.027)
Buyer/recipient top-one share	0.0220 *** (3.964)	0.0298 *** (3.519)	0.0095 * (1.873)
Seller/provider top-three share	0.0066 (0.735)	0.0529 *** (3.589)	0.0018 (0.207)
Buyer/recipient top-three share	0.0250 *** (4.085)	0.0389 *** (2.951)	0.0201 *** (3.728)
Seller/provider dependence	0.0205 ** (2.560)	0.0174 * (1.777)	0.0138 * (1.843)
Buyer/recipient dependence	0.0245 *** (4.294)	0.0317 *** (3.328)	0.0113 ** (2.173)
Seller/provider projected degree	−0.0084 (−0.670)	−0.0659 *** (−3.049)	−0.0021 (−0.227)
Buyer/recipient projected degree	−0.0136 (−1.372)	0.0005 (0.033)	−0.0184 *** (−2.619)
Seller/provider projected closeness	0.0011 (0.099)	−0.0519 ** (−2.397)	−0.0036 (−0.338)
Buyer/recipient projected closeness	0.0023 (0.264)	0.0022 (0.180)	−0.0092 (−0.982)

Note: Direction is taken from the source operation record: seller/provider means that the listed company provides the transaction object, and buyer/recipient means that it receives the transaction object. It is an economic transaction role, not a legally signed cash flow, creditor, or debtor classification. Seller and buyer measures enter jointly within each indicator, while scale, concentration, projected degree, and projected closeness remain in separate specifications to avoid combining conceptually overlapping network measures. All explanatory variables and controls are measured in the exact adjacent year t − 1. Models include firm and year fixed effects and two-way firm-year clustered standard errors. The scale and projected-position models use 22,338 observations; concentration models require both directional layers to be active and use 19,567 observations. Within-pair VIFs range from 1.06 to 2.03. BH and Holm adjustments are evaluated within the 12 direction-scale, 24 direction concentration, and 12 direction projection tests, respectively. ***, **, and * denote significance at the 1%, 5%, and 10% levels.

extends the direction analysis across all three firm-level dimensions. Seller/provider and buyer/recipient measures enter jointly within each indicator, while different indicators remain in separate regressions. For scale, seller/provider and buyer/recipient amounts are both negatively associated with Merton DD (−0.0259 and −0.0410) and KMV DD (−0.0276 and −0.0237), and their relationship counts show the same negative pattern. All eight Merton and KMV scale coefficients retain Benjamini–Hochberg significance at 5% within the 12-test direction-scale family. Relational expansion is therefore associated with a thinner structural buffer on both transaction sides.

Within-role concentration provides the stabilizing side of the same double-edged pattern. All four buyer/recipient concentration measures are positively associated with both Merton and KMV DD, and these eight coefficients survive both Benjamini–Hochberg and Holm correction within the 24-test direction concentration family. Buyer/recipient top-three share is also positive for BhSh DD (0.0201, p < 0.001), while seller/provider top-three share is positive for KMV DD (0.0529, p < 0.001); both survive the two corrections. The result is economically consistent with allocating value through a manageable core of repeatedly used counterparties, thereby improving information, continuity, and resource matching. Its stabilizing content is strongest where counterparty quality, substitutability, and governance sustain those relationships.

Direction-specific projected position is more selective. Seller/provider projected degree is negatively associated with KMV DD (−0.0659, p = 0.002) and survives both corrections within the 12-test direction projection family (BH q = 0.028; Holm p = 0.028). Buyer/recipient projected degree is negative for BhSh DD at the conventional level (−0.0184, p = 0.009), while projected closeness is weaker. The seller/provider result provides the clearest incremental position signal and is consistent with wider common transaction environments increasing monitoring and responsibility allocation complexity. Within-pair correlations and VIFs remain moderate (VIF 1.06–2.03), supporting empirical separation of the paired role estimates. Direction records the disclosed provider/recipient role; legal cash flow and creditor–debtor status can be incorporated as additional contractual layers.

Table 9. Local microstructures and credit risk by transaction type (exact adjacent-year t − 1 specifications).

Variable	Merton Funding & Financial	Merton Goods & Equity	Merton Services & Operations	KMV Funding & Financial	KMV Goods & Equity	KMV Services & Operations
Open V-shaped configuration	−0.0337	−0.0190	0.0028	−0.0254	0.0002	0.0081
Star configuration	−0.1126 ***	−0.0580 **	0.0005	−0.0644 **	−0.0226	0.0365
Bridge: presence	−0.0005	−0.0112	0.0278	−0.0471	−0.0272	−0.0465
Closed 2 × 2: presence	−0.0442	−0.0830 **	−0.0849 **	−0.1345	−0.0145	−0.0255
Bridge: intensity	0.0098	−0.0155	0.0380	−0.1083	−0.0482	−0.0553
Closed 2 × 2: intensity	−0.0285	−0.0323 *	−0.0172	−0.2120 *	−0.0295	0.0154
Observations	16,647	16,480	15,315	16,647	16,480	15,315

Note: Only the three transaction groups with sufficient coverage are reported. Network variables and controls are measured in the exact adjacent year t − 1. All models include state ownership, firm and year fixed effects, and two-way firm-year clustered standard errors. These content layers aggregate both transaction directions; Table 8 separately reports source-coded seller/provider and buyer/recipient scale, concentration, and projected position measures. ***, **, and * denote significance at the 1%, 5%, and 10% levels.

next tests whether local configurations differ across funding/financial, goods/equity, and services/operations layers.

Funding and financial transactions show negative star coefficients for Merton and KMV DD, while closed 2 × 2 intensity is marginally negative for KMV DD. In goods and equity transactions, closed 2 × 2 presence is negatively associated with Merton DD; services and operations show the same negative Merton presence pattern. These layer-specific estimates demonstrate that the credit risk content of a configuration depends on the transaction environment in which it occurs.

Goods, equity, service, and operating transactions differ from loans or guarantees in settlement, pricing, maturity, and substitutability. Table 9 therefore establishes transaction content heterogeneity, while Table 8 provides a complementary role-based decomposition across scale, concentration, and projected position. Negative scale coefficients on both sides are consistent with broader working capital, settlement, coordination, and monitoring demands. Directional concentration is generally positive, especially on the buyer/recipient side, while seller/provider projected degree is negative for KMV DD. Together, these results distinguish the allocation of value among existing partners from the expansion of direct or shared-party reach. A future legal-exposure layer can add creditor-debtor status, repayment terms, guarantee beneficiary, maturity, and pricing.

The transaction-type estimates demonstrate that the credit risk content of local structure varies with the economic setting of the underlying transactions. They therefore serve as boundary evidence that complements the primary network findings.

4.6. Supplementary Channel Correlations

Table 10. Conditional channel correlations linking network measures to KMV distance to default.

Channel	Network Measure	a: Network-Channel Association	b: Channel-DD Association	Conditional Network Coefficient	Product a × b	Sobel z	N
Related-party fund occupation	Total RPT amount	0.073 *** (6.840)	−0.069 *** (−5.254)	−0.031 ** (−2.325)	−0.0050	−4.167	23,579
Related-party fund occupation	Number of related parties	0.059 *** (4.827)	−0.068 *** (−5.185)	−0.054 *** (−3.418)	−0.0040	−3.533	23,579
Resource coordination	HHI	0.037 *** (3.416)	0.034 *** (2.810)	0.022 ** (2.149)	0.0013	2.170	22,779
Within-configuration transaction intensity	Bridge intensity	0.0983 *** (3.441)	−0.0610 *** (−4.763)	−0.0453 (−1.514)	−0.0060	−2.789	23,579

Note: These supplementary channel calculations use the previous available firm observation and firm-clustered standard errors and are reported as exploratory descriptive evidence alongside the exact-adjacent-year primary results. t-statistics for paths a, b, and c’ are in parentheses. The path from the closed 2 × 2 configuration to within-configuration transaction intensity is 0.0226 (t = 0.557), indicating that this particular channel is not supported in the current specification. *** and ** denote significance at the 1% and 5% levels.

reports supplementary channel correlations. Scale measures are paired with related-party fund occupation, HHI with resource coordination, and bridge intensity with within-configuration transaction intensity. The coefficient products and Sobel statistics are used to organize the economic pathways suggested by the baseline results: resource commitment for scale, coordination or dependence for concentration, and common transaction intensity for shared-party structure.

The fund-occupation results help interpret the negative coefficients on network scale. Total RPT amount and the number of related parties are positively associated with fund occupation, which is negatively associated with KMV DD. The indirect effects are negative, with Sobel statistics of −4.167 and −3.533. This pattern is consistent with fund occupation linking broader and larger RPT relationships to a weaker liquidity buffer.

The HHI results point to a different channel. HHI is positively associated with resource coordination, which is positively associated with KMV DD. The indirect effect is 0.0013, with a Sobel statistic of 2.170. Concentration need not represent dependence alone: a stable key relationship may support internal resource matching and lower information and coordination costs. This interpretation still depends on counterparty quality and how transferred resources are used.

The channel patterns differ across the two complex configurations. Bridge intensity is positively associated with within-configuration transaction intensity, which is negatively associated with KMV DD; the coefficient product is −0.0060. The bridge association is therefore most evident when the shared relationship carries a larger transaction amount. For closed 2 × 2 participation, the proposed transaction-intensity channel is imprecisely estimated, while the baseline presence and intensity coefficients remain informative. Repeated connections, cross-exposure, and complex responsibility boundaries offer complementary interpretations for future direct testing.

4.7. Synthesis of the Main Findings by Analytical Dimension

Table 11. Summary of the main findings by analytical dimension.

Analytical Dimension	Structural Component	Representative Measures	Core Finding	Supplementary Evidence or Boundary
Focal-firm network characteristics	Relational scale	Count, total amount, average amount	Negative for Merton and KMV DD; count and total amount are the primary scale findings	The three measures provide complementary summaries of breadth, aggregate commitment, and average tie intensity
	Transaction concentration	HHI, largest-party share, top-three share, dependence index	Top-three share is positively associated with KMV DD; other concentration evidence is weaker	The KMV evidence is strongest; interpretation depends on counterparty quality, substitutability, governance, and period
	Projected position	Degree and closeness centrality	Projected degree has a negative but outcome-dependent association after opportunity controls	Popularity-conditioned, hub-downweighted, top-hub-trimmed, and identifier-only tests retain a negative direction but are supplementary
Local transaction patterns and microstructures	Basic configurations	Open V-shaped, star	Degree-based categories provide a descriptive benchmark; continuous measures offer greater discrimination	The broad star category is interpreted together with continuous degree and formation-opportunity controls
	Shared-counterparty bridge	Presence and intensity	The association is outcome-dependent after the revised timing and inference choices	Reported as secondary evidence; transaction-layer estimates reveal meaningful heterogeneity
	Closed 2 × 2	Presence and intensity	Negative for Merton DD in primary models and for Merton and BhSh DD in the degree-preserving excess-closure tests	The raw coefficient attenuates after projected degree, while excess closure isolates the component above the two-sided degree sequence

synthesizes the evidence under two analytical dimensions. The first three rows concern the focal firm’s scale, concentration, and projected position; the final three concern the local transaction patterns and microstructures in which the firm participates. The negative scale association and positive KMV top-three-share association constitute the central firm-level double-edged findings, while repeated closed 2 × 2 sharing provides the principal local structural signal. Direction, transaction-type, channel, and prediction results sharpen the interpretation and identify the settings in which these headline conclusions are most informative.

The first dimension concerns the focal firm’s own network characteristics. Relational scale is the most stable result: count and total RPT amount are negatively associated with Merton and KMV DD and survive Holm and Benjamini–Hochberg adjustments. Table 8 shows the same negative scale pattern on both seller/provider and buyer/recipient sides. The positive KMV top-three-share association is reinforced by generally positive directional concentration estimates, particularly for the buyer/recipient layer. Projected position is more outcome-dependent, while the negative seller/provider KMV coefficient and the popularity-conditioned, identifier-only, and hub-downweighted estimates consistently associate wider shared-party reach with a thinner credit buffer.

The second dimension concerns local transaction patterns and microstructures. Basic open-V and star categories provide degree-based benchmarks, while bridge results supply secondary evidence. Closed 2 × 2 presence and intensity are negative for Merton DD and survive within-family correction in the primary models. Observed closure greatly exceeds 100 degree-sequence-preserving randomized networks in every year, and excess closure is negatively associated with Merton and BhSh DD after focal scale, projected reach, and counterparty popularity are controlled. Identifier-only and obvious-intragroup exclusion tests add outcome-specific support. Closure thus provides an informative repeated-sharing signal that complements broader shared-counterparty reach and remains distinct from the degree sequence.

Robustness and transaction-layer analyses define the boundary conditions of these conclusions. Scale is comparatively stable across later samples, and the KMV top-three share remains visible. Projected position and closure provide more period- and outcome-specific information, while funding, goods/equity, and services/operations layers produce economically distinct coefficients. These patterns clarify when each network dimension is most informative and strengthen the transaction-content interpretation of the results.

The supplementary channel correlations organize the economic pathways suggested by the baseline findings. Fund occupation is consistent with the scale result, resource coordination with the concentration result, and within-configuration transaction intensity with the bridge result. Future designs can strengthen this evidence by measuring the proposed channels separately in time or linking them to institutional changes and relationship reorganization.

The evidence is organized by inferential strength and economic content. The primary continuous findings are the negative scale associations and the positive KMV top-three-share association. Primary Merton closure results and randomized excess-closure estimates provide structure-sensitive evidence beyond aggregate activity and the degree sequence. Projected position contributes supplementary information because its magnitude varies across outcomes, while hub, popularity, and identifier checks retain a consistent negative direction. Transaction-layer, channel correlation, and prediction analyses clarify where the core findings are most informative.

5. Discussion

The results support a relational interpretation of corporate credit risk in which the organization of disclosed RPTs contributes information about firm-level credit buffers. The empirical scope centers on within-firm changes in relational scale, value allocation, projected position, and local sharing, providing a structured basis for monitoring credit conditions within an evolving transaction system.

5.1. Theoretical Implications

The first implication is the double-edged credit risk content of the three firm-level RPT dimensions. Relationship scale captures the breadth and financial intensity of direct ties; its negative association with DD on both seller/provider and buyer/recipient sides links broader ownership-related exchange to greater coordination, settlement, monitoring, and working capital demands. Concentration captures a different decision: the positive KMV association of the top-three share, reinforced by the directional concentration results, is consistent with stable core relationships improving information, resource matching, and predictability. Projected degree adds indirect reach through shared counterparties, and its negative direction—especially the seller/provider KMV estimate—shows how broader access can coexist with common exposure and more complex responsibility allocation. This three-dimensional pattern reconciles internal capital market and agency perspectives and extends transaction network evidence [9,10] to relationships shaped by ownership, control, and internal capital markets.

The second implication concerns complementarity among shared-counterparty measures. Projected degree captures the breadth of indirect reach through common parties, whereas closed 2 × 2 captures repeated sharing within the same listed-firm neighborhood. Repeated sharing may facilitate verification and coordination while also concentrating settlement dependencies, common exposures, and responsibility allocation demands. Closed participation is associated with lower Merton and BhSh DD in several specifications and remains informative after focal degree, transaction amount, concentration, counterparty popularity, and the degree sequence are benchmarked. The attenuation after projected degree enters is economically consistent with their common shared-party origin, while excess closure identifies unusually repeated sharing as a distinct review signal within broader projected reach.

The channel correlations point to distinct economic pathways: scale is linked to resource commitment and fund occupation, concentration to coordination and dependence, and shared-counterparty structures to common exposure and organizational complexity. Their descriptive role complements the baseline estimates and identifies concrete variables and timing structures for future mechanism tests.

Methodologically, one-mode projection and local closure are overlapping views of shared-counterparty information. The revised joint estimates, counterparty-popularity controls, hub-downweighted projection, identifier-only network, and degree-preserving randomizations make that overlap explicit while isolating an excess-closure component. A future multiplex design could retain transaction type, role direction, legal creditor–debtor status, contractual terms, and controller identity as separate layers [37,38].

5.2. Risk Governance Implications for Complex Financial Systems

The systems-level relevance of the analysis lies in measuring firm-level relational risk within an evolving transaction network. The listed firm-year is the unit of analysis and DD is the outcome, complementing research on financial network reconfiguration around Black Swan events [49] and multiplex contagion across asset layers [37]. This positioning connects observable transaction organization to risk governance while leaving shock-driven network dynamics as a natural next stage of systems research.

For corporate managers, RPT governance should move beyond transaction value thresholds. When related-party count, total amount, and average amount increase together, reviews should focus on non-operating fund occupation by related parties, recovery of related receivables, and cash flow maturity matching. A high concentration ratio should not be interpreted in isolation; assessment also requires the key related party’s operating and financial condition, the fairness of pricing, and the durability of resource coordination.

Creditors, auditors, and regulators can use the results as a layered screening framework. Relationship scale indicates how many ownership-linked ties and how much transaction value require monitoring; the KMV top-three share identifies a concentration pattern consistent with stable coordination among core counterparties. This screening role complements evidence that public communication of audit risks can discipline reporting around related-party transactions [50]. Projected reach and closed 2 × 2 participation identify repeated shared-party environments that warrant closer review, especially when they remain unusual after degree, amount, and hub opportunities are considered. The small rolling-origin error reductions provide modest supporting evidence that the network block can complement financial-statement and market-based credit analysis; however, the negative BhSh out-of-sample R² shows that this incremental predictive content is not uniform across outcomes.

Disclosure design affects which relationships can be identified and monitored. Current reports are organized mainly by transaction or related party, making repeated sharing across listed firms difficult to detect. Standardized related-party identifiers, records of relationship changes, and consistent transaction classifications would improve network identification and preserve traceable data for review and resolution.

5.3. Limitations and Future Research

First, firm and year fixed effects, exact t − 1 timing, and two-way clustered inference strengthen temporal ordering and statistical reliability. Reverse causality and time-varying organizational changes remain important topics for causal extension because distress can reshape RPT organization and reorganizations can jointly affect network measures and DD. Regulatory changes, forced relationship exits, natural-disaster exposure, and business-group reorganizations offer promising sources of plausibly external variation [20].

Second, the new edge-level tests substantially strengthen entity resolution and business-group interpretation. The source-ID subset displays strong within-year name-ID consistency, and identifier-only closure intensity remains negatively associated with BhSh DD. Removing parent, subsidiary, and same-parent edges leaves a negative KMV closure result, showing that the configuration contains information beyond these readily identified intragroup relationships. Ultimate controller links, historical name registries, finance company classifications, and a stratified manually validated benchmark would extend this validation to broader group boundaries and formal precision recall reporting.

Third, the primary annual edge weight measures the total economic intensity of each disclosed relationship, while source direction codes provide seller/provider and buyer/recipient measures for all three firm-level dimensions: scale, concentration, and projected position. Negative scale coefficients on both sides reinforce the relational expansion result; positive directional concentration estimates and the negative seller/provider projected-degree estimate for KMV show that value allocation and shared-party reach carry distinct economic content. Transaction-type subnetworks further demonstrate differences across funding, goods/equity, and service/operating relationships. A directed multiplex extension can add legal creditor–debtor status, loan advance versus repayment, guarantee beneficiary, contractual terms, maturity, and pricing to the observed role direction.

Fourth, the sample and outcome define a clear population boundary. The estimates describe how network organization varies with credit risk among RPT-active firm-years. A future two-part design can extend the analysis to a consistently screened listed-firm population by first modeling RPT participation and then examining network structure among participants. Post-2011, post-2015, period interaction, and within-year rank estimates address long-horizon coverage changes within the present sample (Appendix A Table A7 and Table A12). The rolling-origin holdout exercise provides modest supporting evidence for incremental prediction in Merton and KMV DD, while the negative out-of-sample R² for BhSh DD defines an outcome-specific boundary.

6. Conclusions

This study examines how disclosed RPT relationships organize firm-level credit conditions within a complex financial system. Annual listed-firm related-party bipartite networks for RPT-active Chinese A-share firms preserve three firm-level network dimensions and local shared-counterparty structures over 2003–2024.

The firm-level evidence reveals a clear double-edged pattern across relationship scale, transaction concentration, and projected position. Larger relationship scale is associated with smaller Merton and KMV credit buffers, while broader projected shared-counterparty reach is associated with lower Merton DD in the separate model. In contrast, a higher top-three-related-party share is associated with higher KMV DD, consistent with coordination and predictability among core partners. Direction-specific estimates reinforce all three dimensions: scale is negative on both seller/provider and buyer/recipient sides, concentration is generally positive (especially on the buyer/recipient side), and seller/provider projected degree is negative for KMV DD. The role-based evidence therefore deepens the economic interpretation of the aggregate network results.

The local microstructure evidence identifies repeated closed sharing as the principal structure-sensitive signal. Closed 2 × 2 presence and intensity are negatively associated with Merton DD, while simple degree-based forms and shared-counterparty bridges offer less stable differentiation. Observed closure exceeds degree-sequence-preserving randomized benchmarks, and excess closure remains negatively associated with Merton and BhSh DD after focal scale, projected reach, and counterparty popularity are controlled. Repeated local sharing therefore provides information beyond relationship count and the two-sided degree sequence.

Economic magnitude, direction, transaction layer, identifier, and intragroup checks reinforce these interpretations; the rolling-origin exercise provides modest supplementary predictive evidence and identifies an outcome-specific boundary. Together, they provide a coherent body of conditional firm-level evidence across measurement, timing, and transaction content dimensions.

For research on complex financial systems, transaction connectedness should be assessed through scale, value allocation, projected reach, and local organization rather than through a single connectivity measure. Broad relational expansion may warrant closer review, concentration should be interpreted in light of counterparty quality and governance, and unusually high closure can flag common exposures and unclear responsibility allocation. Future work can extend this firm-level framework with ultimate controller registries, legal creditor–debtor terms, and shock-based designs to examine causal and system-wide dynamics.