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Complex Network Modeling: Theory and Applications, 2nd Edition
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Complex Network Modeling: Theory and Applications, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 10 October 2025 | Viewed by 9639

Special Issue Editor

Dr. Gaogao Dong

E-Mail Website
Guest Editor
School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China
Interests: network science; complex systems; statistical physics; complex system; data science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With the rapid development of information technology, the study of complex networks has become increasingly important and attracted researchers in different fields. Complex network theory, by correlating disorganized information, allows people to quantify and predict the real-world systems accurately. Although a great deal of research has been conducted on complex networks to date, it is still under-researched for various reasons, including the rapid development of science and technology and the explosion of big data. This Special Issue aims to investigate the theory of complex networks, modelling by use of complex networks, and the application of complex networks to multidisciplinary fields.

Submissions of manuscripts on complex network modeling, structure and function analysis, percolation theory; modelling, structural and functional analysis of complex networks; dynamical analysis on complex networks; network control, control and stability of multi-intelligent systems; biological networks, systems biology, biodynamic systems; network analysis of social, economic and technological networks; basic theory and applications of cyber security; complex networks and big data analysis and computation; the intersection of complex systems with other disciplines and their applications, etc. are welcome.

The Special Issue will bring together contributions from researchers in nonlinear dynamics, statistical physics, systems science, computer science, social psychology, communication, and other scientific fields. Papers describing the theoretical studies of principles, as well as new experimental results, are expected.

Dr. Gaogao Dong
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complex network modeling, structure, and function analysis
  • network analysis of social, economic, and technological networks
  • dynamics on complex networks: propagation, games
  • complex networks and big data analytics and computing
  • network security fundamental theory and application
  • complex network applications: link prediction and recommendation algorithms

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Related Special Issue

Published Papers (5 papers)

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Research

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31 pages, 3910 KiB  
Article
Shock Propagation and the Geometry of International Trade: The US–China Trade Bipolarity in the Light of Network Science
by Evangelos Ioannidis, Dimitrios Dadakas and Georgios Angelidis
Mathematics 2025, 13(5), 838; https://doi.org/10.3390/math13050838 - 3 Mar 2025
Viewed by 933
Abstract
What is the impact of geopolitics on the geometry of global trade? What is the key structural role that led to the emergence of the US–China trade bipolarity? Here, we study the geometry of international trade, taking into account not only the direct [...] Read more.
What is the impact of geopolitics on the geometry of global trade? What is the key structural role that led to the emergence of the US–China trade bipolarity? Here, we study the geometry of international trade, taking into account not only the direct but also the indirect trade relations. We consider the self-weight of each country as an indicator of its intrinsic robustness to exogenous shocks. We assess the vulnerability of a country to potential demand or supply shocks based on the entropy (diversification) of its trade flows. By considering the indirect trade relations, we found that the key structural role that led to the emergence of the US–China trade bipolarity is that of the intermediary hub that acts as a “bridge” between different trade clusters. The US and China occupied key network positions of high betweenness centrality as early as 2010. As international trade was increasingly dependent on only these two intermediary trade hubs, this fact led to geopolitical tensions such as the US–China trade war. Therefore, betweenness centrality could serve as a structural indicator, forewarning of possible upcoming geopolitical tensions. The US–China trade bipolarity is also strongly present in self-weights, where a race in terms of their intrinsic robustness to exogenous shocks is more than evident. It is also interesting that the US and China are not only the top shock spreaders but also the most susceptible to shocks. However, China can act more as a shock spreader than a shock receiver, while for the USA, the opposite is true. Regarding the impact of geopolitics, we found that the Russia–Ukraine conflict forced Ukraine to diversify both its exports and imports, aiming to lower its vulnerability to possible shocks. Finally, we found that international trade is becoming increasingly oligopolistic, even when indirect trade relationships are taken into account, thus indicating that a “Deep Oligopoly” has formed. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications, 2nd Edition)
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24 pages, 5916 KiB  
Article
Portfolio Construction: A Network Approach
by Evangelos Ioannidis, Iordanis Sarikeisoglou and Georgios Angelidis
Mathematics 2023, 11(22), 4670; https://doi.org/10.3390/math11224670 - 16 Nov 2023
Cited by 4 | Viewed by 3001
Abstract
A key parameter when investing is Time Horizon. One of the biggest mistakes investors make is not aligning the timeline of their goals with their investment portfolio. In other words, time horizons determine the investment portfolio you should construct. We examine which [...] Read more.
A key parameter when investing is Time Horizon. One of the biggest mistakes investors make is not aligning the timeline of their goals with their investment portfolio. In other words, time horizons determine the investment portfolio you should construct. We examine which portfolios are the best for long-term investing, short-term investing, and intraday trading. This study presents a novel approach for portfolio construction based on Network Science. We use daily returns of stocks that compose the Dow Jones Industrial Average (DJIA) for a 25-year period from 1998 to 2022. Stock networks are estimated from (i) Pearson correlation (undirected linear statistical correlations), as well as (ii) Transfer Entropy (directed non-linear causal relationships). Portfolios are constructed in two main ways: (a) only four stocks are selected, depending on their centrality, with Markowitz investing weights, or (b) all stocks are selected with centrality-based investing weights. Portfolio performance is evaluated in terms of the following indicators: return, risk (total and systematic), and risk-adjusted return (Sharpe ratio and Treynor ratio). Results are compared against two benchmarks: the index DJIA, and the Markowitz portfolio based on Modern Portfolio Theory. The key findings are as follows: (1) Peripheral portfolios of low centrality stocks based on Pearson correlation network are the best in the long-term, achieving an extremely high cumulative return of around 3000% as well as high risk-adjusted return; (2) Markowitz portfolio is the safest in the long-term, while on the contrary, central portfolios of high centrality stocks based on Pearson correlation network are the riskiest; (3) In times of crisis, no portfolio is always the best. However, portfolios based on Transfer Entropy network perform better in most of the crises; (4) Portfolios of all stocks selected with centrality-based investing weights outperform in both short-term investing and intraday trading. A stock brokerage company may utilize the above findings of our work to enhance its portfolio management services. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications, 2nd Edition)
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15 pages, 4185 KiB  
Article
Outer Synchronization of Two Muti-Layer Dynamical Complex Networks with Intermittent Pinning Control
by Yi Liang, Yunyun Deng and Chuan Zhang
Mathematics 2023, 11(16), 3543; https://doi.org/10.3390/math11163543 - 16 Aug 2023
Cited by 5 | Viewed by 1310
Abstract
This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response [...] Read more.
This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response configuration, and sufficient conditions to achieve the outer synchronization are derived based on the Lyapunov stability theory and matrix inequalities. Second, outer synchronization problem of multi-layer networks is discussed by setting an adaptive intermittent pinning controller; an appropriate Lyapunov function is selected to prove the criteria of synchronization between the drive multi-layer network and the response multi-layer network. Finally, three simulation examples are given to show the effectiveness of our control schemes. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications, 2nd Edition)
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Review

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12 pages, 374 KiB  
Review
Exploring the Percolation Phenomena in Quantum Networks
by Chuanxin Wang, Xinqi Hu and Gaogao Dong
Mathematics 2024, 12(22), 3568; https://doi.org/10.3390/math12223568 - 15 Nov 2024
Viewed by 919
Abstract
Quantum entanglement as a non-local correlation between particles is critical to the transmission of quantum information in quantum networks (QNs); the key challenge lies in establishing long-distance entanglement transmission between distant targets. This issue aligns with percolation theory, and as a result, an [...] Read more.
Quantum entanglement as a non-local correlation between particles is critical to the transmission of quantum information in quantum networks (QNs); the key challenge lies in establishing long-distance entanglement transmission between distant targets. This issue aligns with percolation theory, and as a result, an entanglement distribution scheme called “Classical Entanglement Percolation” (CEP) has been proposed. While this scheme provides an effective framework, “Quantum Entanglement Percolation” (QEP) indicates a lower percolation threshold through quantum preprocessing strategies, which will modify the network topology. Meanwhile, an emerging statistical theory known as “Concurrence Percolation” reveals the unique advantages of quantum networks, enabling entanglement transmission under lower conditions. It fundamentally belongs to a different universality class from classical percolation. Although these studies have made significant theoretical advancements, most are based on an idealized pure state network model. In practical applications, quantum states are often affected by thermal noise, resulting in mixed states. When these mixed states meet specific conditions, they can be transformed into pure states through quantum operations and further converted into singlets with a certain probability, thereby facilitating entanglement percolation in mixed state networks. This finding greatly broadens the application prospects of quantum networks. This review offers a comprehensive overview of the fundamental theories of quantum percolation and the latest cutting-edge research developments. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications, 2nd Edition)
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27 pages, 456 KiB  
Review
Dynamics of Social Influence and Knowledge in Networks: Sociophysics Models and Applications in Social Trading, Behavioral Finance and Business
by Dimitris Tsintsaris, Milan Tsompanoglou and Evangelos Ioannidis
Mathematics 2024, 12(8), 1141; https://doi.org/10.3390/math12081141 - 10 Apr 2024
Cited by 4 | Viewed by 2511
Abstract
In this paper we offer a comprehensive review of Sociophysics, focusing on relevant models as well as selected applications in social trading, behavioral finance and business. We discuss three key aspects of social diffusion dynamics, namely Opinion Dynamics (OD), Group Decision-Making (GDM) and [...] Read more.
In this paper we offer a comprehensive review of Sociophysics, focusing on relevant models as well as selected applications in social trading, behavioral finance and business. We discuss three key aspects of social diffusion dynamics, namely Opinion Dynamics (OD), Group Decision-Making (GDM) and Knowledge Dynamics (KD). In the OD case, we highlight special classes of social agents, such as informed agents, contrarians and extremists. As regards GDM, we present state-of-the-art models on various kinds of decision-making processes. In the KD case, we discuss processes of knowledge diffusion and creation via the presence of self-innovating agents. The primary question we wish to address is: to what extent does Sociophysics correspond to social reality? For that purpose, for each social diffusion model category, we present notable Sociophysics applications for real-world socioeconomic phenomena and, additionally, we provide a much-needed critique of the existing Sociophysics literature, so as to raise awareness of certain issues that currently undermine the effective application of Sociophysics, mainly in terms of modelling assumptions and mathematical formulation, on the investigation of key social processes. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications, 2nd Edition)
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