The Interplay of Network Architecture and Performance in Supply Chains: A Multi-Tier Analysis of Visible and Invisible Ties

Abstract

While supply chain competition increasingly occurs at the network level, most research remains limited to dyadic or triadic relationships, failing to capture the full complexity of multi-tier supply networks. This research investigates the influence of four distinct types of network ties—contractual, transactional, professional, and personal—on supply chain performance, evaluated across five dimensions: cost, quality, delivery, flexibility, and innovation. The analysis draws on data gathered from 153 component-level supply networks, encompassing a total of 1852 entities within South Korea’s automotive and electronics manufacturing sectors. We employed social network analysis with a directed-valued network approach to capture asymmetric relationships. Results reveal that network architecture affects performance dimensions differently: centralized professional knowledge sharing enhances delivery performance, while concentrated personal ties prove detrimental; for innovation, dense network connections and dominant transactional hubs unexpectedly hinder performance by fostering conformity; cost performance shows mixed effects, with transactional centralization impeding efficiency while professional and personal leadership facilitates cost reduction. The influence of the original equipment manufacturer on supplier selection moderates these relationships, particularly mitigating negative impacts of personal tie centralization. These findings challenge conventional assumptions about network density benefits and demonstrate that supply network competence—the ability to configure and leverage network architecture—requires careful consideration of multiple tie types and their distinct effects on different performance outcomes.

1. Introduction

Supply chains are complex, multilevel systems with structured architectures that encompass a broad range of organizations, people, and activities, all interconnected through the exchange of materials, information, and resources to produce products and deliver them to the end customer [1,2]. They can also be described as a series of value-adding processes carried out by distinct yet well-aligned entities across multiple tiers. This alignment yields benefits greater than the sum of what each individual participant could achieve on their own and ensures those benefits are shared among all participants [3]. Taken together, these notions imply that a supply chain is best analyzed as a multi-tier network of entities.

Prior research indicates that inter-firm networks—encompassing both direct and indirect connections—are instrumental in shaping a company’s competitive edge and overall outcomes. In line with the resource-based view, various studies have used different network metrics to demonstrate that the configuration of a firm’s partner network can systematically affect its outcomes. For example, strong inter-organizational networks have been linked to improvements in organizational learning [4], innovation [5,6,7], new venture survival [8,9], team creativity [10], and financial performance [11,12]. This ability to develop and leverage inter-firm relationships for better results is often termed network competence [13,14]. The widespread adoption of the network competence perspective prompts several key questions for scholars in this field: To what extent does the configuration of a firm’s supply network influence its performance? Which specific structural characteristics within that network serve to improve or weaken performance outcomes? Moreover, in what ways might an original equipment manufacturer’s (OEM’s) effort to influence suppliers’ sourcing decisions interact with such mechanisms?

To address these questions, this study how several key indices that characterize a supply network’s architecture impact five major supply chain performance dimensions: cost, quality, delivery, flexibility, and innovation. In addition, it accounts for the contingent effects of an OEM’s involvement in selecting non-immediate suppliers. By utilizing a unique dataset capturing supply networks with directed, weighted relationships, this research extends the traditional network competence view to the broader supply chain context. In doing so, the study introduces a supply network competence perspective, an approach to understanding how the structural properties of an entire supply network—beyond any single inter-firm relationship—can systematically shape a firm’s performance outcomes.

However, capturing supply network architecture in a meaningful way requires attention to the types of interorganizational ties that structure relationships across firms. While prior research has advanced our understanding of supply networks, it has largely concentrated on formal and easily observable ties—such as contractual or transactional relationships—often limited to first-tier suppliers. This focus overlooks the broader structure of multi-tier networks and the diversity of relational mechanisms that connect firms throughout the supply base. In response, this study develops a framework that distinguishes interorganizational ties into four types—contractual, transactional, professional, and personal—and examines how these operate across multiple tiers. By incorporating both visible and less visible ties, our approach offers a more comprehensive representation of supply network architecture and its implications for operational performance.

The rest of the paper first outlines prior research streams on network competence, providing the foundation for formulating the hypotheses on supply network competence. It then proceeds to describe, in Section 3, the dataset, measurement constructs, and methodological approach employed to test these hypotheses. Section 4 reports the empirical findings, covering both descriptive network patterns and regression analyses. Finally, Section 5 offers concluding remarks, highlighting the key findings, theoretical and practical implications, limitations, and avenues for future inquiry.

2. Theoretical Background and Hypotheses

2.1. Network Competence Perspective

Within the literature of network competence, two principal research streams can be distinguished. One stream adopts an ego-centric view, focusing on how a particular firm’s position in an inter-organizational network affects its network competence. The other stream takes a socio-centric view, concentrating on the overall structural pattern of relationships encompassing multiple firms in the network. Proponents of the ego-centric perspective posit that a firm’s network position largely determines its ability to acquire and assimilate resources, thereby influencing its performance. Accordingly, scholars argue that a firm occupying a particularly advantageous position in a network can more readily tap into resources and leverage them for better performance [15]. Established supply chain management studies—especially those examining dyadic or triadic supply chain relationships—support this ego-centric view. They find that a focal firm’s interactions with its immediate partners significantly shape that firm’s actions and outcomes.

By contrast, the socio-centric perspective broadens the focus from an individual firm’s position to the architecture of the entire inter-firm network. This view treats the network as a form of governance system that directly affects performance, on the premise that multiple independent entities are collaborating toward a common goal of optimizing overall system performance [16]. Using the network as the unit of analysis enables researchers to capture the full complexity of an interlinked network of firms, rather than just isolated organizations within it. Applying the network competence lens to the supply chain context is therefore useful for analyzing the architecture of supply networks and understanding their performance outcomes. Accordingly, the present study adopts a socio-centric approach to examine how an OEM’s supply network properties relate to performance, extending the network competence perspective. Based on our review, large-scale empirical investigations linking an OEM’s socio-centric supply network competence to its performance outcomes remain scarce.

2.2. Supply Network Ties and Indices

Extensive research in corporate governance recognizes that inter-firm networks—composing both inter-organizational and interpersonal ties—serve as unique, inimitable sources of resources and capabilities for firms [17,18]. However, an aspect often neglected in prior studies is the multiplex nature of inter-organizational and interpersonal ties embedded in an inter-firm network. Multiplexity refers to the presence of multiple types and attributes of network ties co-existing within the same network [19,20,21,22]. In other words, a single supply network can encompass various kinds of connections, each with distinct characteristics. To uncover the “hidden” properties of a supply network’s architecture, it is essential to adopt a multiplexity perspective that accounts for these different dimensions of network ties. Accordingly, our analysis focuses on four distinct forms of ties within supply networks—contractual, transactional, professional, and personal—that connect participating partners. The first two types represent visible, formal connections through tangible resources such as goods, services, and financial exchanges are transacted. In contrast, the latter two types capture less visible, intangible exchanges among network members.

Table 1. Conceptual definitions, item measures, and related literature for supply network tie type. (Adapted from [19,20]).

Network Tie Type	Conceptual Definition	Item Measure	Related Literature
Contractual tie	The extent to which a supply network entity perceives that it has a “complete” formal written contract with its immediate counterpart	We have a formal written contract(s) detailing the operational requirements. We have a formal written contract(s) that detail(s) how performance will be monitored.	[23,24,25]
		We have a formal written contract(s) detailing warranty policies.
		We have a formal written contract(s) detailing how to handle complaints and disputes (e.g., penalties for contract violations).
		We have a formal written contract(s) detailing the level of service expected from this supplier.
Transactional tie	The amount of “monetary” exchange (in percentage points) between a supply network entity and its immediate counterpart(s)	For OEMs (i.e., tier-0 firms): A percentage of total spending for each tier-1 supplier of the selected component.	[24,26,27]
		For tier-(N) (i.e., intermediate) suppliers where N = 1 or 2: Percentages of total sales derived from the tier- (N − 1) buyer AND total spending for each tier- (N + 1) supplier in dealing with the OEM’s selected component.
		For tier-3 (i.e., end-tier) suppliers: A percentage of total sales derived from tier-2 suppliers in dealing with the OEM’s selected component.
Professional tie	A supply network entity’s perceived strength of the interactions with its immediate counterpart in performing “work responsibilities”	We regularly communicate (via face-to-face interaction, conference calls, e-mails, etc.) on work matters.	[24,25,28]
		We widely share and welcome each other’s ideas or initiatives via open communication (e.g., joint workshops, etc.).
		Communication between us occurs at different levels of management and cross-functional areas.
		I (or our executives) receive periodic feedback (via face-to-face meetings, conference calls, email, etc.) on progress, problems, and plans from this supplier’s counterparts.
		I (or our executives) make periodic on-site visits to this supplier’s plants.
Personal tie	A supply network entity’s perceived strength of the interactions “not directly related to work” with its immediate counterpart	We often invite each other to participate in various social activities.	[29,30,31,32]
		We do personal favors for each other. We voluntarily exchange something of a personal nature to each other on appropriate occasions (e.g., birthday cards, congratulations, condolences, etc.).
		We often communicate (via face-to-face meetings, phone calls, emails, social network services, etc.) during non-working hours.
		We often communicate (via face-to-face, phone calls, emails, social network services, etc.) outside workplaces.

provides conceptual definitions for each of these four tie types, along with measurement items drawn from the extant literature.

Complementing Table 1, Figure 1 visually illustrates how the four tie types manifest within the same component-level supply network. The network shown is drawn from our dataset and represents a consumer electronics manufacturer (OEM) with three first-tier (T1), five second-tier (T2), and four third-tier (T3) suppliers. Each panel in the figure depicts the same set of firms and tiers but with edges differentiated by tie type. This comparison highlights how the topology of the same underlying supply base varies substantially depending on the nature of the interorganizational relationship, thereby motivating the need to quantify these structural patterns using formal network metrics.

To quantify the structural properties of supply networks formed by these various tie types, we employ social network analysis (SNA) indices. Such metrics, commonly used in organizational behavior and strategic management research, allow us to rigorously measure the architecture of a supply network for each tie type. More precisely, the analysis concentrates on four socio-centric metrics—betweenness centralization, in-degree centralization, out-degree centralization, and the global clustering coefficient—that capture overarching structural configuration of interactions among multiple network actors. In contrast to much of the existing literature, which typically treats all connections as homogeneous and symmetrical, this study applies a directed-valued network perspective accounts for both the direction and strength of ties, providing a more nuanced and realistic representation of supply network architectures [33,34]. These socio-centric measures were selected for their theoretical and methodological strengths in capturing global structural features across networks of varying sizes. In contrast to density or ego-centric indices, centralization and clustering coefficients are relatively robust to minor differences in the number of nodes or tiers, making them appropriate for cross-network comparisons [35,36]. Furthermore, as detailed in Section 3.1, the data collection process was carefully designed to bound the size and depth of networks across firms. This sampling strategy, combined with the use of globally normalized SNA metrics, helps ensure the comparability and consistency of the analysis despite small variations in supplier composition.

Prior research in organizational network theory suggests that different types of interorganizational ties are grounded in distinct relational mechanisms and structural logics [37]. Building on this foundation, our analysis treats these relational dimensions as distinct—not only in terms of their functional roles and visibility, but also in their structural embeddedness within the network. To assess the empirical validity of these distinctions, we conducted one-way ANOVA tests on key SNA metrics across tie types. The results revealed statistically significant differences in network characteristics by tie type. Moreover, all pairwise Pearson correlation coefficients among structural indices remained below 0.85, consistent with thresholds proposed by [38] to mitigate multicollinearity concerns. Together, these findings reinforce the analytical separation of the four tie types adopted in this study.

2.3. Hypotheses

A supply network’s activities are orchestrated through micro- and macro-level planning, control, and adjustments. Consequently, much of the literature views an OEM’s supply chain performance indicators as aggregate outcomes of the overall system, realized through the OEM’s role as the firm interfacing directly with end-customers, together with all the other members embedded in its supply network [39,40]. This perspective implies that performance should be evaluated at the network level, reflecting the combined contributions of the entire web of interconnected firms. Despite the general use of conventional performance measures, it is important to distinguish the cost dimension from the other performance dimensions (quality, delivery, flexibility, and innovation) because they behave differently in a networked setting. From the OEM’s standpoint, cost reductions achieved by its direct or indirect partners can be readily transmitted to, and reflected in, the OEM’s own cost performance metrics [41,42]. In practice, this means that an OEM can reap at least some benefits from an upstream partner’s improved cost efficiency, even if other partners in the network do not attain similar gains. By contrast, the other four performance measures—quality, delivery, flexibility, and innovation—are more systematic in nature and require system-wide alignment for improvements to translate across the network. An individual member’s enhancement in any of these areas do not automatically improve the OEM’s overall performance unless all relevant network members are able to keep pace with the improvement [43,44,45]. In a supply network, one or a few firms attaining excellence in quality, delivery, flexibility, and innovation do not automatically translate into improved performance for the OEM or the network as a whole; any gains are constrained by the least prepared partner (a bottleneck) that cannot match those improvements. In light of this distinction between cost and other dimensions, the study formulates a series of research hypotheses regarding the performance implications of key supply network architectural indices.

In SNA, an actor’s betweenness centrality reflects the degree to which it lies on the shortest paths between other actors, serving as an intermediary that can control resource flows. The network-level counterpart, betweenness centralization, indicates the extent to which the entire network revolves around a select group of hub actors, measured by the variation in betweenness centrality across all firms in the network [35,46]. This structural property can have varying effects on an OEM’s performance. On one hand, if a supply network’s connections are largely channeled through a particular subset of focal firms (high betweenness centralization), those hub firms can secure a disproportionate share of network resources—such as favorable contract terms, larger transactions, or extensive professional and personal contacts—and thus achieve greater cost advantages. The OEM, in turn, can indirectly benefit from the cost efficiencies gained by these influential upstream partners.

On the other hand, for performance dimensions like quality, delivery, flexibility, and innovation, an OEM’s outcomes improve when network resources are more evenly distributed (i.e., betweenness centralization is low). In a network with low betweenness centralization, no single group of firms monopolizes the intermediary positions, which allows resources, information, and problem-solving insights to flow more freely among a broad range of partners. In this more egalitarian structure, the OEM can draw upon a wider array of shared knowledge, capabilities, and technological breakthroughs from its network members [6]. Based on this reasoning, the following hypotheses are proposed:

Hypothesis 1A.

The betweenness centralizations of an OEM’s supply network, comprising contractual, transactional, professional, and personal ties, are positively associated with its cost performance.

Hypothesis 1B.

The betweenness centralizations of an OEM’s supply network, comprising contractual, transactional, professional, and personal ties, are negatively associated with its quality, delivery, flexibility, and innovation performance.

In network terms, an actor’s in-degree centrality is the number of ties directly toward it, reflecting how many other entities provide resources or connections to that actor. In-degree centralization is the socio-centric measure derived from the variance in actors’ in-degree centralities, indicating the degree to which incoming network resources are concentrated in particular actors at the network level [36]. A network entity receiving a large number of incoming ties is one upon which many others depend. Research suggests that when a firm is less dependent on others’ resources (because it attracts resources from many partners), it can leverage this resource dominance to more effectively achieve its objectives [47,48]. In the context of cost performance, if a few focal firms receive the bulk of resource inflows, they may more easily realize cost efficiencies (e.g., economies of scale or favorable input pricing) that will be reflected in the OEM’s cost metrics. Similarly, when a particular group of forms holds a greater share of the network’s resources, those firms are likely to have the power to act as coordinators or catalysts, tailoring network-wide goals in ways that optimize their unique, path-dependent performance results. This line of reasoning leads to the following hypothesis:

Hypothesis 2.

The in-degree centralizations of an OEM’s supply network, comprising contractual, transactional, professional, and personal ties, are positively associated with its cost, quality, delivery, flexibility, and innovation performance.

Out-degree centrality refers to the number of ties an actor directs outward to others, and out-degree centralization captures the extent to which a few actors dominate in disseminating resources to the rest of the network [36]. In an inter-firm network, high out-degree centralization means that a small cluster of focal firms is responsible for supplying or sharing resources with most other members. In such a scenario, the majority of firms, reliant on resources from this small cluster, are neither able nor inclined to take initiative in coordinating network-level objectives—since the network’s resource flow is essentially one-way. In terms of cost performance, if only a limited group of firms are providing resources to everyone else, those few providers may deplete their own resources or bandwidth hindering their ability to achieve cost benefits. Following the inverse logic of the in-degree centralization argument, we propose:

Hypothesis 3.

The out-degree centralizations of an OEM’s supply network, comprising contractual, transactional, professional, and personal ties, are negatively associated with its cost, quality, delivery, flexibility, and innovation performance.

Direct connections between a firm and its partners (e.g., customers or suppliers) facilitate efficient resource exchange and distribution, contributing to competitive advantage for the firms involved [49,50]. The overall connectedness of a network can be measured by the global clustering coefficient, which indicates how cliquish or tightly knit the network is as a whole (i.e., the prevalence of closed triangles or group links among firms) [51,52]. A highly connected (strongly clustered) supply network implies that many partners are directly linked with one another. Such connectivity can enhance path-dependent performance measures (like quality, delivery, flexibility, and innovation) by serving as a conduit for better alignment and coordination across the network. Well-connected networks enable quicker information sharing, joint problem-solving, and collective innovation, all of which support these performance dimensions. However, from the OEM’s point of view, an excessively high degree of connectivity might introduce redundant interactions, additional coordination effort, and higher overhead costs. Because an OEM can often reap cost benefits from its network without needing to be densely interconnected with all partners, overly cliquish networks may actually diminish cost performance by increasing complexity and coordination costs. Accordingly, we hypothesize:

Hypothesis 4A.

The global clustering coefficients of an OEM’s supply network, comprising contractual, transactional, professional, and personal ties, are negatively associated with its cost performance.

Hypothesis 4B.

The global clustering coefficients of an OEM’s supply network, comprising contractual, transactional, professional, and personal ties, are positively associated with its quality, delivery, flexibility, and innovation performance.

In a supply network composed of independent entities each pursuing its own interests, there is a risk of opportunistic behavior—firms may act to maximize their individual performance without regard for mutual benefits or reciprocity [24]. The expansion of outsourcing and offshoring has increased the number of indirect and more distant suppliers in many networks, making some partners invisible to the OEM and difficult to monitor. One way an OEM can curb opportunistic tendencies among these indirect upstream members is to exert strong influence over its immediate (tier-1) suppliers’ sourcing decisions [19,53]. By guiding or controlling whom its direct suppliers select as their own partners, the OEM can indirectly govern the broader network. In terms of cost outcomes, such influence allows the OEM to capture more of the non-path-dependent benefits (i.e., cost performance) generated anywhere in its supply network, because the OEM’s preferences can trickle down through procurement choices. More broadly, a supply network can be viewed as a deliberately designed system that is aligned with the OEM’s strategic intent(s) [19,54]. When an OEM actively shapes its immediate suppliers’ behaviors (including their choice of sub-suppliers), it can effectively disseminate and enforce network-wide objectives for performance improvements in areas like quality, delivery, flexibility, and innovation. This influence can amplify the positive impact of network resources on the OEM’s performance by ensuring that even indirect contributors operate in line with the OEM’s goals . Thus, we propose:

Hypothesis 5.

An OEM’s influence on its immediate suppliers’ sourcing decisions positively moderates the associations between the architectural properties of the supply network and its cost, quality, delivery, flexibility, and innovation performance.

3. Methodology

This study investigates how the structural configuration of multi-tier supply networks influences a range of operational performance outcomes. The analysis employs network-level measures as explanatory variables in regression models, enabling the assessment of how variations in supply network architecture correspond differences in performance across complex, interconnected ecosystems. A whole network approach is adopted to capture both visible and invisible structural patterns, providing a systemic perspective on supply chain design and its performance implications.

3.1. Data

Following established recommendations for social network research [55,56], we employed a survey-based quantitative approach to collect detailed data on an OEM’s component-level network, capturing both the direction and strength of ties among all participating supply network partners [57,58,59]. This whole-network perspective has been consistently advocated as the most effective method for examining the systemic architecture of supply networks [55,60]. To reduce the burden of data collection while maintaining comparability across cases, three global South Korean manufacturers—two in consumer electronics and one in the automotive sector—were engaged, and a combined fixed list and snowball sampling strategy was implemented [61]. The executive contacts at each participating firm were first asked to identify a strategically important component with a network of manageable scope—defined as no more than three tiers and roughly five suppliers per tier—and to nominate the sourcing manager most knowledgeable about that component. This step ensured that the selected networks were both strategically significant and comparable in depth and size, while also reducing key informant bias by directing the survey to individuals with operational knowledge of the focal supply network [62]. Each nominated sourcing manager, typically based at the OEM or focal firm, then evaluated their primary immediate suppliers (usually those on the firm’s preferred supplier list) across four types of ties: contractual, transactional, professional, and personal. The first three tie types were measured using five-point Likert scales, while transactional ties were quantified as the percentage of the focal firm’s total spending (or the supplier’s sales) related to the selected component. Using contact information provided by the focal firm’s manager, the same survey was subsequently administered to each first-tier supplier, who in turn assessed their own immediate suppliers (tier two) on the same tie dimensions. This iterative process was repeated for successive tiers until the end-tier suppliers in the component’s network were reached.

To avoid duplicate responses, surveys for a given tier were conducted only after completing data collection for the preceding tier. Given the highly sensitive nature of the information, respondents were assured that all answers would be treated as strictly confidential and that results would be reported only in aggregate form. All completed questionnaires were collected directly by the first author, without being routed through the buying firms, to further reinforce confidentiality. This process yielded a unique dataset comprising 153 component-level networks—89 electronics and 64 mechanical—with a total of 1852 network members.

3.2. Variables and Measures

3.2.1. Network Indices

We employed a directed-valued network framework that accounts for both the direction and strength of each tie between network entities. Formally, a directed-valued network consists of a set of actors (or nodes) $\left\{{\mathrm{n}}_1,{ \mathrm{n}}_2, \cdots , {\mathrm{n}}_{\mathrm{g}}\right\}$, a set of arcs (i.e., directional ties or links) $\left\{{\mathrm{l}}_1,{ \mathrm{l}}_2, \cdots , {\mathrm{l}}_{\mathrm{L}}\right\}$, and a set of values $\left\{{\mathrm{v}}_1,{ \mathrm{v}}_2, \cdots , {\mathrm{v}}_{\mathrm{L}}\right\}$ assigned to those arcs, such that ${\mathrm{l}}_{\mathrm{k}} = \text{<}{\mathrm{n}}_{\mathrm{i}},{\mathrm{n}}_{\mathrm{j}}\text{>} \text{≠} {\mathrm{l}}_{\mathrm{m}} = \text{<}{\mathrm{n}}_{\mathrm{j}},{\mathrm{n}}_{\mathrm{i}}\text{>}$, and where ${\mathrm{v}}_{\mathrm{k}}$ is not necessarily equal to ${\mathrm{v}}_{\mathrm{m}}$. This representation is particularly useful in analyzing supply network structures because it captures the possibility that a focal firm and its suppliers may perceive the strength—or even existence—of their ties differently. Consequently, there is increasing demand for SNA metrics that are specifically formulated for use within directed-valued network contexts, which require a different adjacency matrix.

In particular, this study centers on four socio-centric network measures—betweenness centralization, in-degree centralization, out-degree centralization, and the global clustering coefficient—that capture how all actors within a defined network boundary are structurally arranged. These indices were selected because they capture distinct dimensions of global network structure that are theoretically meaningful across different types of supply network ties. Out-degree centralization, for example, indicates the extent to which outbound connections (such as transactions or information flows) are concentrated in a few nodes, suggesting potential control points or systemic bottlenecks. Betweenness centralization reflects the reliance on intermediaries to connect otherwise distant nodes, revealing possible structural vulnerabilities. Clustering captures the degree of local closure, often associated with redundancy and coordination efficiency. Together, these metrics have been widely used in organizational and interorganizational network research to assess structural properties related to control, coordination, and resilience [36,46,55]. Although ego-centric measures such as centrality focus on the network position of a single actor (the ego), they provide valuable insights into directed-valued networks by recognizing that one actor’s view of the network architecture can differ substantially from those of others connected directly or indirectly [35,63].

First, betweenness centralization reflects whether network actors share central positions relatively evenly or whether certain actors (i.e., hubs) occupy disproportionately central roles. This metric is computed as the ratio of the observed variance in betweenness centrality to the maximum possible variance for a network of the same size [46]. Betweenness centrality itself is an ego-centric measure that counts how frequently an actor appears on the shortest paths between all possible pairs of other actors, highlighting its role as an intermediary. From a socio-centric perspective, betweenness centralization ranges from 0—indicating that all actors have equal betweenness centrality—to 1, where a single actor lies on every shortest path linking the others. In this study, we compute the betweenness centralization for a directed-valued supply network by adopting the formula proposed in [64] for weighted betweenness centrality (${\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)$), for network actor ${\mathrm{n}}_{\mathrm{i}}$, defined as follows:

$${\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)={\displaystyle \frac{{\mathrm{g}}_{{\mathrm{n}}_{\mathrm{j}}{\mathrm{n}}_{\mathrm{k}}}^{\mathrm{w}\mathsf{\alpha }}({\mathrm{n}}_{\mathrm{i}})}{{\mathrm{g}}_{{\mathrm{n}}_{\mathrm{j}}{\mathrm{n}}_{\mathrm{k}}}^{\mathrm{w}\mathsf{\alpha }}}}$$

(1)

where ${\mathrm{g}}_{{\mathrm{n}}_{\mathrm{j}}{\mathrm{n}}_{\mathrm{k}}}^{\mathrm{w}\mathsf{\alpha }}$ is the total number of geodesics between two actors (${\mathrm{n}}_{\mathrm{j}}$ and ${\mathrm{n}}_{\mathrm{k}}$), ${\mathrm{g}}_{{\mathrm{n}}_{\mathrm{j}}{\mathrm{n}}_{\mathrm{k}}}^{\mathrm{w}\mathsf{\alpha }}({\mathrm{n}}_{\mathrm{i}})$ is the number of geodesics passing through actor ${\mathrm{n}}_{\mathrm{i}}$, and $\mathsf{\alpha }$ is a positive tuning parameter that is set to the benchmark value of 0.5 to equally value both the number of ties and their strengths ($\mathrm{w}$). Thus, betweenness centralization can be formally expressed as

$${\mathrm{C}}_{\mathrm{B}}={\displaystyle \frac{\sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}{\max \sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}}$$

(2)

where ${\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)$ is the largest value of the betweenness centrality that occurs across the network $\mathrm{G}$; that is, ${\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)=\underset{\mathrm{i}}{\max }{\mathrm{C}}_{\mathrm{B}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)$.

Table 2. (a) Structural implications of betweenness centralization by tie type. (b) Structural implications of in-degree centralization by tie type. (c) Structural implications of out-degree centralization by tie type. (d) Structural implications of global clustering coefficient by tie type. (Adapted from [19,20]).

(a)
Socio-Centric SNA Index	Tie Type	Implications for Directed Valued Supply Network
Betweenness centralization	Contractual tie	The extent to which there exist particular focal firms that have more or less complete (or specific) contract terms than other supply network members. - The lower the index, the more firms there are that have more equally complete contract terms with their supply network counterparts. - The higher the index, the more firms there are that have more unequally complete contract terms with their supply network counterparts.
	Transactional tie	The extent to which there exist particular focal firms that have a higher or lower percentage of monetary exchanges than other suppliers’ network members (i.e., distribution of sales and spending in the network). - The lower the index, the more firms there are that have equal percentages of monetary exchanges with their supply network counterparts. - The higher the index, the more firms there are that have higher or lower percentages of monetary exchange with their supply network counterparts.
	Professional tie	The extent to which there exist particular focal firms that have more or less work-related interactions than other supply network members. - The lower the index, the more firms there are that have equal amounts of work-related interactions with their supply network counterparts. - The higher the index, the more firms there are that have more or less work-related interactions with their supply network counterparts.
	Personal tie	The extent to which there exist particular focal firms that have more or less non-work-related interactions than other supply network members. - The lower the index, the more firms there are that have equal amounts of non-work-related interactions with their supply network counterparts. - The higher the index, the more firms there are that have more or less non-work-related interactions with their supply network counterparts.
(b)
Socio-centric SNA index	Tie type	Implications for directed valued supply network
In-degree centralization	Contractual tie	The extent to which particular focal firms have more complete (i.e., less favorable) contract terms than the other supply network members. - The lower the index, the more firms there are that have fair contract terms with their supply network counterparts. - The higher the index, the fewer particular focal firms possess less favorable contract terms with their supply network counterparts.
	Transactional tie	The extent to which particular focal firms take up a greater percentage of the monetary exchanges occurring inside the supply network than others. - The lower the index, the more firms there are that have equal percentages of the monetary exchanges. - The higher the index, the fewer particular focal firms account for higher percentages of the monetary exchanges than the others.
	Professional tie	The extent to which particular focal firms have more incoming work-related interactions than the rest of the supply network members. - The lower the index, the more equal the amount of work-related interactions between supply network members. - The higher the index, the more work-related interactions among supply network members is focused on fewer particular focal firms.
	Personal tie	The extent to which particular focal firms have more incoming non-work-related interactions than the rest of the supply network members. - The lower the index, then each of the supply network members has a more equal amount of non-work-related interactions with one another. - The higher the index, the more non-work-related interactions among supply network members are focused on fewer particular focal firms.
(c)
Socio-centric SNA index	Tie type	Implications for directed valued supply network
Out-degree centralization	Contractual tie	The extent to which particular focal firms provide more complete (i.e., less favorable) contract terms for the rest of the supply network members. - The lower the index, the more firms there are that have fair contract terms with their supply network counterparts. - The higher the index, the fewer particular focal firms yield less favorable contract terms for their supply network counterparts.
	Transactional tie	The extent to which particular focal firms generate a higher percentage of the monetary exchanges occurring within the supply network than others. - The lower the index, the more firms there are that have equal percentages of the monetary exchanges. - The higher the index, the fewer particular focal firms send out higher percentages of the monetary exchanges for the rest of the supply network members.
	Professional tie	The extent to which particular focal firms have more outgoing work-related interactions to the rest of the supply network members. - The lower the index, the more equal the amount of work-related interactions between each of the supply network members and the others. - The higher the index, the fewer particular focal firms initiate most of the work-related interactions with the rest of the supply network members.
	Personal tie	The extent to which particular focal firms generate more outgoing non-work-related interactions for the rest of the supply network members. - The lower the index, then each of the supply network members has a more equal amount of non-work-related interactions with one another. - The higher the index, the fewer particular focal firms make more non-work-related interactions for the rest of the supply network members.
(d)
Socio-centric SNA index	Tie type	Implications for directed valued supply network
Global clustering coefficient	Contractual tie	The extent to which members of the entire supply network are directly connected by contract relations. - The lower the index, the lower the proportion of supply network members that are directly connected by contract relationships (i.e., the supply network has a more “hierarchical” architecture as a whole). - The higher the index, the higher the proportion of supply network members that are directly connected by contract relationships (i.e., the supply network has a more “lateral” architecture as a whole).
	Transactional tie	The extent to which the members of the entire supply network are directly connected by monetary exchanges. - The lower the index, the more the supply network as a whole has a “hierarchical” architecture in the monetary exchanges among supply network members. - The higher the index, the more the supply network as a whole has a “lateral” architecture in the monetary exchanges among supply network members.
	Professional tie	The extent to which all the supply network members freely communicate work-related subjects across firm boundaries. - The lower the index, the more supply network as a whole has a “hierarchical” architecture for work-related interactions among supply network members. - The higher the index, the more the supply network as a whole has a “lateral” architecture for work-related interactions among supply network members.
	Personal tie	The extent to which all the supply network members freely communicate non-work-related subjects across firm boundaries. - The lower the index, the more “hierarchical” the architecture of non-work-related interactions among members in the supply network as a whole. - The higher the index, the more “later” the architecture of non-work-related interactions among members in the supply network as a whole.

a illustrates how betweenness centralization manifests across the four tie types. While the mathematical index captures variation in brokerage roles, its interpretation differs by relational context. In contractual ties, high centralization implies that few firms dominate formal governance. For transactional ties, it may indicate control over monetary flows. In professional or personal ties, central actors may broker knowledge or informal influence. These distinctions are critical to understanding how similar structural patterns can yield different performance effects depending on the underlying tie type.

In the case of a directed network, two additional degree indices can be defined as follows: in-degree, the number of links terminating at the actor (${\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}$), and out-degree, the number of ties originating from the actor (${\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}$) [36]. In-degree centralization calculates the dispersion or variation in in-degree centrality and the extent of an individual actor’s influence on other actors. Thus, high in-degree centralization indicates that the incoming flows of different network resources are focused on a small group of actors within the overall network. Likewise, high out-degree centralization reflects a network structure in which a limited set of actors distribute the majority of their resources to others in the network. In this study, the in-degree and out-degree centralization of a supply network are computed from the in-degree centrality (${\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)$) and out-degree centrality (${\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)$) of actor ${\mathrm{n}}_{\mathrm{i}}$ in a directed-valued network, as defined by the following formulas [64]:

$${\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)={\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}\text{×}{\left({\displaystyle \frac{{\mathrm{s}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}}{{\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}}}\right)}^{\mathsf{\alpha }}$$

(3)

$${\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)={\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}\text{×}{\left({\displaystyle \frac{{\mathrm{s}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}}{{\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}}}\right)}^{\mathsf{\alpha }}$$

(4)

where ${\mathrm{s}}^{\mathrm{in}}$ and ${\mathrm{s}}^{\mathrm{out}}$ denote the summed strengths of all incoming and outgoing ties, respectively. Thus, the general in-degree and out-degree centralization measures—each taking a value between 0 to 1—are formulated as follows:

$${\mathrm{C}}_{\mathrm{D-in}}={\displaystyle \frac{\sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}{\max \sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}}$$

(5)

$${\mathrm{C}}_{\mathrm{D-out}}={\displaystyle \frac{\sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}{\max \sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}}$$

(6)

where ${\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)$ and ${\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)$ are the largest in-degree and out-degree centrality values in the network $\mathrm{G}$.

In the case of a directed network, two additional degree indices can be defined: in-degree, the number of links terminating at the actor (${\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}$), and out-degree, the number of ties originating from the actor (${\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}$) [36]. In-degree centralization measures the dispersion or variation in in-degree centrality, indicating the extent to which an individual actor influences other actors. Thus, high in-degree centralization indicates that the incoming flows of different network resources are concentrated in a small group of actors within the overall network. In a similar vein, high out-degree centralization reflects a situation in which a few actors distribute the majority of their network resources to others in the system. In this study, the measure of in-degree and out-degree centralization for a supply network are calculated from the in-degree centrality (${\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)$) and out-degree centrality (${\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)$) of actor ${\mathrm{n}}_{\mathrm{i}}$ within a directed-valued network, as determined by the following equations [64]:

$${\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)={\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}\text{×}{\left({\displaystyle \frac{{\mathrm{s}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}}{{\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{in}}}}\right)}^{\mathsf{\alpha }}$$

(7)

$${\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)={\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}\text{×}{\left({\displaystyle \frac{{\mathrm{s}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}}{{\mathrm{k}}_{{\mathrm{n}}_{\mathrm{i}}}^{\mathrm{out}}}}\right)}^{\mathsf{\alpha }}$$

(8)

where ${\mathrm{s}}^{\mathrm{in}}$ and ${\mathrm{s}}^{\mathrm{out}}$ denote the aggregate strengths of all incoming and outgoing ties, respectively. Accordingly, overall in-degree and out-degree centralization values—which fall within a range from 0 to 1—are expressed as:

$${\mathrm{C}}_{\mathrm{D-in}}={\displaystyle \frac{\sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}{\max \sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}}$$

(9)

$${\mathrm{C}}_{\mathrm{D-out}}={\displaystyle \frac{\sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}{\max \sum _{\mathrm{i}\text{∈}\mathrm{G}}\left\{{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)-{\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}_{\mathrm{i}}\right)\right\}}}$$

(10)

where ${\mathrm{C}}_{\mathrm{D-in}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)$ and ${\mathrm{C}}_{\mathrm{D-out}}^{\mathrm{w}\mathsf{\alpha }}\left({\mathrm{n}}^{*}\right)$ represent the maximum in-degree and out-degree centrality scores observed within the network $\mathrm{G}$.

Table 2b presents how in-degree centralization applies across the four tie types. This index captures the extent to which incoming ties—whether contracts, transactions, or communications—are concentrated on a few focal firms. Depending on the tie type, such convergence can reflect different forms of dependency or influence, such as reliance on a few major suppliers or centralized flows of technical input.

Table 2c illustrates the implications of out-degree centralization for each tie type. Here, the focus shifts to how outgoing ties are distributed—highlighting firms that actively disseminate resources or information. While structurally similar to in-degree centralization, the managerial implications differ: high out-degree in transactional ties may indicate financial dominance, whereas in professional or personal ties, it may signify proactive coordination or social brokerage.

Lastly, this study applies the global clustering coefficient (GCC), a metric ranging from 0 to 1, to capture the degree of overall cohesion among actors [51,52]. In SNA, this reflects the likelihood that two actors, ${\mathrm{n}}_{\mathrm{j}}$ and ${\mathrm{n}}_{\mathrm{k}}$, are directly connected when both share a connection with ${\mathrm{n}}_{\mathrm{i}}$, denoted collectively as $\left({\mathrm{n}}_{\mathrm{i}};{\mathrm{n}}_{\mathrm{j}},{\mathrm{n}}_{\mathrm{k}}\right)$. Within a directed-valued network framework, the GCC—treated as a socio-centric indicator—is calculated as the sum of the values of all triplets (i.e., sets of three actors where every actor is linked to the other two; ${\mathrm{\tau }}_{\text{∆}}$) divided by the sum of the value of all triplets (i.e., sets where at least one actor is linked to the other two; $\mathrm{\tau }$). The value of each triplet ($\mathsf{\omega }$) is determined using the geometric mean of the tie strengths among its constituent actors. Formally, the general GCC (${\mathrm{C}}_{\mathrm{g}}$) is given by:

$${\mathrm{C}}_{\mathrm{g}}={\displaystyle \frac{1}{\mathrm{N}}}{\sum }_{\mathrm{i},\mathrm{j},\mathrm{k}\text{∈}\mathrm{G}}\left\{{\displaystyle \frac{{\sum }_{({\mathrm{n}}_{\mathrm{i}};{\mathrm{n}}_{\mathrm{j}},{\mathrm{n}}_{\mathrm{k}})\text{∈}\left\{{\mathrm{\tau }}_{\text{∆}}\right\}}{\mathsf{\omega }}_{{\mathrm{\tau }}_{\text{∆}}}({\mathrm{n}}_{\mathrm{i}};{\mathrm{n}}_{\mathrm{j}},{\mathrm{n}}_{\mathrm{k}})}{{\sum }_{({\mathrm{n}}_{\mathrm{i}};{\mathrm{n}}_{\mathrm{j}},{\mathrm{n}}_{\mathrm{k}})\text{∈}\left\{\mathrm{\tau }\right\}}{\mathsf{\omega }}_{\mathrm{\tau }}({\mathrm{n}}_{\mathrm{i}};{\mathrm{n}}_{\mathrm{j}},{\mathrm{n}}_{\mathrm{k}})}}\right\}$$

(11)

where $\mathrm{N}$ denotes the total count of possible triplets within network $\mathrm{G}$. Additional details on this computational approach can be found in [65].

Table 2d summarizes how the global clustering coefficient applies to the four tie types. This index captures the extent to which firms form tightly connected triads. While high clustering often implies cohesion, its interpretation varies across relational contexts—for example, dense contractual ties may support standardization, whereas dense personal ties could foster informal coordination or redundant communication.

This framework extends beyond the existing network analysis approaches in two important ways. First, while previous frameworks typically assumed homogeneous and symmetrical network ties, our framework explicitly incorporates both the direction and strength of ties to characterize the supply network architecture. This directed-valued network approach allows us to capture the asymmetric nature of supply chain relationships. Second, the framework systematically integrates both the visible (contractual and transactional) and invisible (professional and personal) dimensions of network ties, providing a more comprehensive view of the supply network architecture than traditional frameworks, which focus primarily on formal business relationships. Such a multifaceted approach is necessary to fully capture the complex and multiplex nature of modern supply networks, in which performance outcomes are influenced by the interplay of various types of relationships operating simultaneously across multiple tiers.

3.2.2. Measurement of Performance Outcomes and OEM Influence on Sourcing Decisions

This study employed established and validated scales from prior research to measure five conventional dimensions of supply chain performance and one contextual variable—OEM influence. All multi-item constructs were assessed using a five-point Likert scale. For cost, quality, delivery, and flexibility performance, the anchors were “1” (significantly worse), “3” (neither better nor worse), and “5” (significantly better). For innovation performance and OEM influence, the anchors ranged from “1” (strongly disagree) to “3” (neither agree nor disagree) to “5” (strongly agree). To evaluate measurement quality, confirmatory factor analysis (CFA) was conducted for all constructs based on multi-item reflective indicators. As shown in

Table 3. Confirmatory factor analysis results.

Construct and Measurement Items	Factor Loading	AVE	Composite Reliability	Cronbach’s Alpha
Cost performance		0.734	0.776	0.932
Acquisition costs	0.782
Cost reduction performance	0.911
Designing cost out of the component	0.886
Ability to meet target costs	0.894
Supplier’s ability to engage in strategic cost modeling	0.795
Quality performance		0.792	0.876	0.951
Technical capability	0.831
Conformance quality	0.903
Internal process quality	0.925
Component durability	0.907
Component reliability	0.894
Delivery performance		0.648	0.892	0.813
On-time delivery	0.731
Manufacturing lead time	0.875
Customer lead time	0.802
Shipping accuracy	0.543
Flexibility performance		0.752	0.924	0.891
Volume flexibility	0.854
Delivery flexibility	0.906
Design flexibility	0.868
Launch flexibility	0.840
Innovation performance		0.506	0.754	0.807
By sourcing this component, our firm could significantly increase the number of new products on the market	0.796
By sourcing this component, our firm could add many more new features to existing product(s).	0.759
By sourcing this component, our firm could add unique features to existing product(s).	0.667
By sourcing this component, our firm could have a significantly higher new product success rate.	0.704
By sourcing this component, our firm could develop new product(s) or features much faster.	0.679
OEM’s influence		0.847	0.965	0.960
Our firm maintains active communication with all supply network partners regarding our sourcing strategy.	0.924
Our firm and immediate (i.e., tier-1) suppliers always make joint decisions on selecting tier-2 or 3 suppliers.	0.981
Our immediate (i.e., tier-1) suppliers must obtain our firm’s approval for their selection of tier-2 or tier-3 suppliers.	0.976
Our firm puts significant efforts into aligning suppliers across the whole supply network with our sourcing strategy.	0.746
Our firm has well-established guidelines to support our immediate (i.e., tier-1) suppliers’ selection of suppliers.	0.973

Note: N = 153 component-level networks; Cronbach’s alpha ≥ 0.80; Average variance extracted [AVE] ≥ 0.50; Composite reliability ≥ 0.70; Factor loading ≥ 0.50.

, the factor loadings were statistically significant, confirming that the indicators correspond well with their intended theoretical constructs. All average variance extracted (AVE) values exceeded the recommended threshold of 0.50, supporting convergent validity. Discriminant validity was examined by comparing the squared correlations between each construct pair to their respective AVE values; in all cases, the squared correlations were lower, satisfying the discriminant validity criterion. Reliability was further confirmed using Cronbach’s alpha and composite reliability (CR). All constructs exhibited Cronbach’s alpha values greater than 0.80 and CR values above 0.70, indicating strong internal consistency. Collectively, these results demonstrate that the measurement models possessed sound psychometric properties.

3.3. Methods

Hierarchical multiple regression was employed to evaluate both the main effects and the interaction models (i.e., H1–H5), controlling for the types of component and the overall network size for each component-level supply network. Prior to running these analyses, the OEM’s performance scores across the five supply chain dimensions were transformed into weighted composite values, using factor loadings obtained from the CFA. This weighting procedure was applied because raw ordinal ratings (e.g., from five-point Likert scale) can yield limited statistical precision in certain parametric analyses [27]. Following the guidelines in [66], the control variables were entered in the first step of the regression. In the second step, the primary network architecture indices were added. In the final step, the interaction terms—formed as cross-products between each network index and the OEM’s influence on its immediate suppliers’ sourcing decisions—were introduced. This three-step procedure was repeated across 20 separate regression models; four using the network indices (betweenness centralization, in-degree centralization, out-degree centralization, and the GCC) and five using the performance measures (cost, quality, delivery, flexibility, and innovation) as dependent variables. All continuous predictors were mean-centered to aid interpretation and to reduce potential multicollinearity in moderated regression models [67,68,69]. Variance inflation factors (VIFs) were calculated for each model, with the highest VIF observed being 3.173, well below the threshold for multicollinearity concerns.

4. Results and Interpretations

The hypotheses were evaluated using the above-described hierarchical regression framework. The results linking component-level supply network architecture to OEM supply chain performance are presented in

Table 4. Result of hierarchical regression analysis: effects of betweenness centralizations.

	Dependent Variables
	Cost			Quality			Delivery			Flexibility			Innovation
Steps	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
Comp	−0.020	−0.019	−0.017	0.009	0.011	0.006	0.008	0.019	0.024	0.045	0.039	0.039	−0.074	−0.082	−0.088
Size	0.012	0.011	0.010	0.005	0.005	0.005	−0.002	−0.002	−0.004	0.004	0.004	0.004	0.001	0.001	−0.001
(a)		1.347	1.496		1.339	2.228		1.662	0.752		−0.994	−0.148		−2.358	−2.515
(e)		−0.420	−0.705		−3.048	−3.359		0.364	0.621		1.305	1.225		−2.068 *	−2.163 **
(i)		−0.138	0.034		0.234	0.262		−1.223	−1.064		0.817	0.818		0.671	0.709
(m)		0.132	0.315		0.211	0.427		−2.090 *	−2.312 **		−1.036	−0.811		0.747	0.493
(a) × OFI			−6.606			−7.926			9.437			−1.374			4.756
(e) × OFI			−0.434			4.945			−4.352			6.653 *			0.024
(i) × OFI			0.875			−1.103			−0.917			−0.136			−4.674 ***
(m) × OFI			0.505			−1.932			−5.612 **			−0.530			2.803
F	0.276	0.182	0.375	0.050	0.861	1.01	0.016	2.79 **	2.33 **	0.286	0.629	0.723	0.688	1.867 *	1.801 *
R2	0.004	0.007	0.026	0.001	0.034	0.066	0.000	0.103	1.41	0.004	0.025	0.048	0.009	0.071	0.113

Notes: N = 153 component-level networks; Control variables: comp = component type; size = network size. Independent variables: (a) contractual, (e) transactional, (i) professional, and (m) personal betweenness centralization. Moderator: OFI = OEM’s influence on tier-1 suppliers’ sourcing decisions. The figures shown are unstandardized coefficients. * p < 0.10; ** p < 0.05; *** p < 0.01.

(H1A and H1B),

Table 5. Result of hierarchical regression analysis: effects of in-degree centralizations.

	Dependent Variables
	Cost			Quality			Delivery			Flexibility			Innovation
Steps	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
Comp	−0.020	−0.022	−0.034	0.009	0.004	−0.006	0.008	0.009	0.005	0.045	0.025	0.012	0.012	−0.084	−0.087
Size	0.012	0.017	0.022	0.005	0.001	0.004	−0.002	−0.009	−0.009	0.004	0.004	0.009	0.009	0.003	0.001
(b)		2.858	3.411		−2.110	−1.492		0.758	1.089		−1.693	−0.651		−2.456	−1.788
(f)		0.852	0.177		1.462	0.686		5.793 **	5.261 *		8.142 ***	7.214 ***		0.558 *	−0.263 *
(j)		−1.117	−1.320		−0.411	−0.437		1.804	2.015 *		−0.836	−0.740		−0.461	−0.052
(n)		−1.879	−1.988		1.294	1.338		0.085	0.298		−3.044	−2.862		−1.800	−1.513
(b) × OFI			4.332			0.223			−5.014			−3.313			−0.743
(f) × OFI			−11.225			−6.449			1.421			1.888			7.701
(j) × OFI			−2.222			−3.235			−2.270			−7.379 **			−3.371
(n) × OFI			1.599			1.900			1.102			3.819			−7.623
F	0.276	0.457	0.637	0.050	0.222	0.384	0.016	3.093 ***	1.934 **	0.286	1.681	1.758 *	0.688	1.558 *	1.387 *
R2	0.004	0.018	0.043	0.001	0.009	0.026	0.000	0.113	0.120	0.004	0.065	0.110	0.009	0.060	0.089

Notes: N = 153 component-level networks; Control variables: comp = component type; size = network size. Independent variables: (b) contractual in-degree centralization, (f) transactional in-degree centralization, (j) professional in-degree centralization, and (n) personal in-degree centralization. Moderator: OFI = OEM’s influence on tier-1 suppliers’ sourcing decisions. The figures shown are unstandardized coefficients. * p < 0.10; ** p < 0.05; *** p < 0.01.

(H2),

Table 6. Result of hierarchical regression analysis: effects of out-degree centralizations.

	Dependent Variables
	Cost			Quality			Delivery			Flexibility			Innovation
Steps	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
Comp	−0.020	−0.013	−0.027	0.009	0.007	0.010	0.008	0.008	−0.004	0.045	0.045	0.046	−0.074	−0.071	−0.051
Size	0.012	0.016	0.014	0.005	0.000	−0.003	−0.002	−0.009	−0.008	0.004	0.003	0.002	0.001	0.005	0.004
(c)		−0.311	−0.251		0.785	1.023		1.813	1.680		−0.995	−0.887		−0.607	−0.428
(g)		−1.312 *	−1.399 *		−0.011	−0.051		−0.743	−0.771		−0.228	−0.283		0.059	0.092
(k)		5.566	5.906 *		−2.963	−2.636		2.427 *	2.422 *		−1.889	−1.870		−3.853	−3.974
(o)		2.455	2.863 *		−2.854	−2.327		−2.797	−2.861		−1.680	−1.747		1.073	1.130
(c) × OFI			−0.586			4.002			−3.982			4.619			4.218
(g) × OFI			0.259			−2.023			1.177			2.701			−1.654
(k) × OFI			10.74			14.26 *			−6.200			7.350			−9.250
(o) × OFI			10.78 **			11.80			−1.529			2.201			−2.968
F	0.276	0.986	1.258	0.050	0.001	1.297	0.016	2.331 **	1.656 *	0.286	0.361	0.685	0.668	1.374	1.248
R2	0.004	0.039	0.081	0.001	0.025	0.084	0.000	0.087	0.104	0.004	0.015	0.046	0.009	0.053	0.081

Notes: N = 153 component-level networks; Control variables: comp = component type; size = network size. Independent variables: (c) contractual out-degree centralization, (g) transactional out-degree centralization, (k) professional out-degree centralization, and (o) personal out-degree centralization. Moderator: OFI = OEM’s influence on tier-1 suppliers’ sourcing decisions. The figures shown are unstandardized coefficients. * p < 0.10; ** p < 0.05; *** p < 0.01.

(H3), and

Table 7. Result of hierarchical regression analysis: effects of global clustering coefficient.

	Dependent Variables
	Cost			Quality			Delivery			Flexibility			Innovation
Steps	1	2	3	1	2	3	1	2	3	1	2	3	1	2	3
Comp	−0.020	−0.027	−0.033	0.009	0.015	0.012	0.008	0.033	0.036	0.045	0.047	0.049	−0.074	−0.100	−0.104
Size	0.012	0.006	0.002	0.005	0.000	−0.002	−0.002	−0.006	−0.003	0.004	−0.001	0.000	0.001	0.012	0.007
(d)		−2.655 *	−3.341 **		−0.525	−0.832		0.306	0.091		−0.158	−0.685		1.144	0.992
(h)		−1.900	−2.232		0.327	0.140		3.202	3.457		−0.551	−0.502		−3.606 *	−3.721 *
(l)		1.924	2.773		1.468	1.863		−3.544	−3.774		3.847	3.948		−1.945	−0.932
(p)		1.572	1.652		1.980	1.999		1.631	1.711		2.427	2.641		−4.261 **	−4.028 **
(d) × OFI			1.207			0.092			5.216			6.336			−1.579
(h) × OFI			−5.441			−2.091			−6.366			−2.165			2.691
(l) × OFI			−1.987			−0.713			1.927			−2.295			−9.968
(p) × OFI			−6.713			−3.203			2.024			−3.465			−6.888 **
F	0.276	0.716	1.009	0.050	0.291	0.292	0.016	1.298	1.097	0.286	0.397	0.573	0.688	2.524	1.897 *
R2	0.004	0.029	0.066	0.001	0.012	0.020	0.000	0.051	0.072	0.004	0.016	0.039	0.009	0.094	0.118

Notes: N = 153 component-level networks; Control variables: comp = component type; size = network size. Independent variables: (d) contractual global clustering coefficient; (h) transactional global clustering coefficient; (l) professional global clustering coefficient; and (p) personal global clustering coefficient. Moderator: OFI = OEM’s influence on tier-1 suppliers’ sourcing decisions. The figures shown are unstandardized coefficients. * p < 0.10; ** p < 0.05; *** p < 0.01.

(H4A and H4B). The moderating role of OEM influence on tier-1 supplier sourcing decisions (H5) was tested for each of these relationships. For interpretive clarity, the discussion primarily reports the estimated coefficients (B) and their statistical significance, while model-level statistics such as F and R² are included in the tables for completeness. This approach offers a holistic view of how network-structural properties are associated with diverse operational outcomes. To protect confidentiality, company names, specific products, and component details are withheld.

4.1. Cost Performance Effects of Supply Network Architecture

Our cost performance analysis revealed mixed results across different network tie types. While most network characteristics showed limited effects, out-degree centralization demonstrated significant but varying impacts depending on the tie type: transactional out-degree centralization negatively affected OEM cost performance, while professional and personal out-degree centralization showed positive effects. Although the overall model did not reach statistical significance, the findings collectively indicate that the multiplex nature of supply network relationships matters in determining cost performance outcomes. These results contradict those of previous studies [40,41,42], which has posited that cost advantages are readily transferable across the broader network. Instead, the results here may suggest that cost performance tends to be inherently localized, with benefits more likely to be realized and shared within relatively confined structures, such as such as dyadic or triadic supply chain relationships. As one senior purchasing executive from an automotive OEM made the following comment to illustrate this point:

“Those (cost benefits generated by downstream suppliers) should be theoretically transferable. In the automobile industry, most cost benefits come from manufacturing process rationalization, capacity management, and/or workforce coordination (e.g., efficient work shifts), which are internal. Further, suppliers will never want to announce this to their counterparts to keep all benefits inside their own. We (i.e., an OEM) thus cannot realize what cost improvements were made (or not) by our suppliers, and this invisibility gets worse when dealing with non-immediate suppliers. This is why we set cost reduction goals every 2–3 years and often offer incentives to encourage suppliers to achieve those goals.”

These results collectively suggest that the multiplex nature of supply network relationships matters. While having a few focal firms dominate the distribution of monetary resources (high transactional out-degree centralization) negatively affects cost performance, having certain firms take leadership in disseminating professional knowledge and building personal relationships (high professional and personal out-degree centralization) demonstrates positive effects. This finding highlights the importance of considering the diverse types of network relationships when designing a supply network architecture for cost efficiency.

4.2. Quality Performance Effects of Supply Network Architecture

As with cost performance, none of the models testing the relationship between quality performance and the supply network indices—whether based on contractual, transactional, professional, or personal ties—yielded statistically significant overall results. While certain coefficients aligned with the proposed hypothesis, the patterns were not robust. Notably, the interaction effects between an OEM’s influence and the extent of professional and personal connections within the network displayed significant positive associations with quality performance. Nevertheless, the models as a whole lacked statistical significance. These outcomes are somewhat puzzling and counterintuitive, given the substantial body of total quality management literature emphasizing the benefits of strong inter-organizational and interpersonal linkages. One purchasing manager from a consumer electronics OEM remarked in this context:

“I believe it is coming from the measure: quality. The qualities of sourced components are continuously traced and tested along the entire supply chain, from raw material suppliers to our tier-1 suppliers. Therefore, you would not be able to find any notable quality increase or decrease within sourced components if you measure our (OEM’s) performance only—those aspects will be more visible at a more downstream level. Most of our quality problems occur rather in assembly lines where all components are gathered.”

4.3. Delivery Performance Effects of Supply Network Architecture

The findings point to subtle linkages between delivery performance and the structural configuration of supply networks, especially with respect to betweenness and in-degree centralization across various tie types. For instance, betweenness centralization within the network of personal ties displayed a negative coefficient (B = −2.312, p < 0.05) in relation to an OEM’s delivery performance. This suggests that delivery outcomes tend to deteriorate when a small number of focal firms act as dominant intermediaries for informal, nonwork-related exchanges among supply chain personnel. From a managerial standpoint, such personal connections are largely intangible and, therefore, challenging to monitor or influence directly. The significant negative interaction coefficient (B = −5.612, p < 0.05) provides an interesting perspective on mitigating the risks associated with personal interactions being concentrated among a small subset of supply network actors. Specifically, the analysis indicates that the adverse influence of personal ties on delivery performance is lessened when the OEM exercises greater authority over its suppliers’ selection of sub-suppliers. In practice, this means that an OEM can offset the drawbacks of high betweenness centralization in personal ties by actively shaping first-tier suppliers’ sourcing decisions for lower-tier partners. Although this effect emerged for only one dependent variable, it is noteworthy in demonstrating how personal relationships among supply chain personnel can play a role in managing traditional delivery performance metrics. In addition, the in-degree centralization of transactional ties shows a positive relationship with the focal OEM’s delivery performance (B = 5.261, p < 0.05). This suggests that: (1) a smaller number of focal firms become key sales points for other network members, (2) these firms can aggregate and coordinate orders across multiple supply chain tiers, and (3) this coordination ultimately enhances the OEM’s delivery performance. This pattern further implies that OEMs can help dampen upstream amplification (or the bullwhip effect) by encouraging a select group of downstream suppliers to place larger, consolidated orders from the broader supply base. Finally, the in-degree and out-degree centralizations of professional ties within the supply network (B = 2.015 and 2.422, respectively; p < 0.1) are both positive and significant. This indicates that delivery performance tends to improve when a concentrated set of focal firms either receive (in-degree) or disseminate (out-degree) a greater share of work-related interactions. These findings are consistent with established evidence that centralized control in supply chains can enhance delivery performance [70,71]. Collectively, the results suggest that OEMs may boost delivery outcomes by fostering a group of suppliers that serve as hubs for collecting and/or distributing professional, work-oriented communications to the rest of the network.

4.4. Flexibility Performance Effects of Supply Network Architecture

The shows that the in-degree centralization of transactional ties within the supply network has a significant positive effect on the OEM’s flexibility performance (B = 7.214, p < 0.01). This finding suggests that when a smaller number of focal firms handle a greater proportion of financial transactions across the network, the OEM is better able to respond to changes in volume, delivery, product design, and new product launches. Combined with the earlier result linking in-degree centralization of transactional ties to stronger delivery performance, this pattern may indicate that (1) these focal firms are leveraging the financial stability derived from higher levels of incoming monetary flows, and (2) the resulting advantages translate into greater flexibility for the OEM and potentially for other members of the supply network.

4.5. Innovation Performance Effects of Supply Network Architecture

The most striking observation for innovation performance concerns the negative consequences of the in-degree centralization in transactional ties within the supply network. While this structural feature was shown earlier to support delivery performance, the results here indicate that concentrating purchasing power in a small number of downstream suppliers can undermine innovation outcomes. One possible explanation is that innovation often depends on dispersed knowledge assets and diverse resource pools—conditions that cannot be met when the OEM relies heavily on only a few dominant suppliers, especially in the current environment of distributed innovation (e.g., crowdsourcing). At the same time, the positive association between betweenness centralization of transactional ties and innovation performance suggests that focal firms acting as critical intermediaries in monetary exchanges can enhance an OEM’s innovation capabilities. In such cases, a select group of network actors—those with substantial roles in both purchasing and sales—may be better positioned to initiate and drive innovation for the benefit of their end customers. This reflects a “more resources, more responsibility” scenario, where well-positioned intermediaries leverage their influence to foster innovative outcomes. Complementing this, the negative coefficient for the GCC of transactional ties reveals that innovation performance declines as the network becomes more laterally interconnected in terms of monetary exchanges. In other words, when many entities have direct transactional relationships with one another, the OEM’s ability to achieve innovation suffers. This finding reinforces the earlier point that innovation gains often arise from a concentrated group of actors rather than a highly interconnected network. It also stands in contrast to earlier work [6], which reported a positive relationship between an OEM’s direct ties and its innovation outcomes. Taken together, the results imply that both excessive density and the presence of dominant hubs—especially when transactional and personal ties intersect—can create structural constraints that limit innovation potential. In such cases, the usual benefits of direct relationships, such as knowledge transfer, spillovers, and information sharing, may be offset or even outweighed by the transaction costs required to establish and sustain those connections. Another possible explanation can be found in the conformance perspective of tightly knit networks. When supply network members are densely connected through transactional and personal ties (i.e., a high GCC), they may develop shared norms and similar thought patterns that encourage conformity rather than divergence. This homogenization of perspectives can inhibit the emergence and sharing of radical ideas that often drive innovation. The finding that an OEM’s influence over its immediate suppliers’ sourcing choices weakens the observed relationship lends additional support to this interpretation. A stronger OEM influence may reinforce this conformance tendency by adding another layer of standardization to the already tightly connected network. Notably, [6] employed a binary and ego-centric measure of degree centrality, whereas the present research applies directed-valued, socio-centric network metrics, offering a more refined understanding of how supply network architecture relates to performance.

5. Conclusions

In an era where competition increasingly occurs between entire supply chains, a central question arises: why do some supply chains outperform others? Although an expanding body of research highlights the coordinated management of inter-firm relationships as a key determinant, much of the existing work remains limited in scope and fails to capture the complexity of multi-tiered supply networks. The present study addresses these gaps by leveraging unique research contexts and an extensive dataset of 153 supply networks comprising 1852 total network members, thereby moving beyond the constraints of prior dyadic or triadic analyses. The dataset originates from the first author’s doctoral dissertation [14], which involved a large-scale survey of component-level supply networks spanning multiple tiers. While subsequent studies have drawn on the same underlying dataset, each pursued distinct research objectives and analytical approaches. For instance, one study [19] examined strategic intents as predictors of network architecture, with separate analyses for the automotive and electronics sectors; another [6] investigated the effects of undirected counts of direct and indirect ties on innovation performance; and a further study [20] provided a descriptive comparison of how directed-valued network ties across multiple tiers vary by type, without making causal inferences. In contrast, the present research employs network architecture measures as explanatory variables and evaluates their associations with multiple dimensions of performance. These distinctions in research scope, model formulation, and performance metrics ensure that the current work does not duplicate the analyses or conclusions of earlier works.

Our social network and hierarchical regression analyses revealed several key findings that advance our understanding of the supply network architecture. First, our analysis of cost performance demonstrates that when network resources are concentrated in the hands of a few firms that distribute them to others (high out-degree centralization), the effects vary by tie type. Transactional out-degree centralization negatively affects OEM’s cost performance, while professional and personal out-degree centralization show positive effects. This suggests that while having a few dominant firms controlling monetary flows may impede cost efficiency, having certain firms take leadership in professional knowledge sharing and personal relationship building can facilitate cost reduction across the network. Second, our analysis of delivery performance identified multifaceted patterns across different network structures and tie types: personal ties concentrated among a few focal firms (high-betweenness centralization) negatively impact the OEM’s delivery performance, but this negative effect can be mitigated through a stronger OEM influence on supplier selection. Moreover, both incoming monetary flows and professional interactions focused on particular firms (high transactional and professional in-degree centralization) positively affect delivery performance, as do professional knowledge-dissemination activities by certain firms (high professional out-degree centralization). These findings collectively suggest that while personal relationships should be decentralized, centralizing both monetary transactions and professional interactions can enhance delivery performance by enabling better coordination and control of material flows through key network entities that serve as consolidation points for resource and knowledge sharing. Third, and perhaps most intriguingly, our findings revealed contrasting effects of network structures on innovation performance: while dense network connections (high GCC) can hinder innovation performance, particularly for transactional and personal ties, having transactional ties concentrated among hub firms (high betweenness centralization) also exhibits negative effects. These findings challenge the traditional view that dense network connections and powerful intermediaries invariably lead to improved knowledge sharing and innovation outcomes. Instead, our results suggest that excessive structural constraints, whether through dense interconnections or dominant hubs controlling transactional flows, foster conformity and reduce idea diversity in networks. This tendency appears to be further reinforced when the OEM exerts a stronger influence on supplier selection, as evidenced by the negative moderating effects.

Given the exploratory stage of empirical research on supply networks, several limitations merit acknowledgment—each offering avenues for future investigation. First, the four tie types considered here do not represent an exhaustive set of possible interorganizational connections. Second, this study relied on a subset of available socio-centric SNA indices to characterize network structures; this choice reflects the study’s emphasis on providing an empirically grounded examination of real-world supply networks. Third, the analysis was based on cross-sectional data, as longitudinal network information was unavailable. Greater access to secondary data sources could enhance the generalizability of findings, though this may require trading off sample size in order to capture complete network data. One possible approach to address this constraint would be to repeat the original data collection with the same respondents after a set period and conduct an event-study analysis to detect abnormal shifts in network characteristics. Finally, the present study uses OEM-level supply chain performance as a proxy for overall network performance. While this approach is supported by theoretical and empirical precedents, a valuable extension would be to compare performance effects at two levels of analysis: the current OEM-centric measures versus outcomes aggregated across multiple firms in the network.