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Complexity of Social Networks
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Complexity of Social Networks

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 31 March 2026 | Viewed by 2522

Special Issue Editors

Prof. Dr. Zi-Ke Zhang

E-Mail Website
Guest Editor
College of Media and International Culture, Zhejiang University, Hangzhou 310058, China
Interests: complex networks; computational social science; social networks; recommender systems; complex systems
Dr. Junming Huang

E-Mail Website
Guest Editor
Paul and Marcia Wythes Center on Contemporary China, Princeton University, Princeton, NJ, USA
Interests: computational social science; social networks; AI; complex systems
Dr. Xiaoke Xu

E-Mail Website
Guest Editor
Center for Computational Communication Research (Zhuhai), School of Journalism and Communication, Beijing Normal University, Beijing, China
Interests: social robots; computational communication; complex networks; social network analysis; big data analysis
Dr. Quanhui Liu

E-Mail Website
Guest Editor
College of Computer Science, Sichuan University, Chengdu 610065, China
Interests: data science; network science; computational epidemiology; graph neural networks; natural language processing

Special Issue Information

Dear Colleagues,

Social networks are characterized by heterogeneous structures, nonlinear dynamics, and evolving interactions among individuals, groups, and communities. Studying these networks is essential for understanding information diffusion, opinion evolution, and collective behavior in digital societies. Recent advances in computational methods have leveraged complex network theory to uncover the underlying mechanisms, including influence propagation, misinformation diffusion, and network evolution.

Digital platforms, such as social media and recommender systems, play vital roles in shaping communication and interactions. Through algorithmic mediation, these platforms impact information flows, influence user behavior, and contribute to the emergence of echo chambers and polarization, significantly promoting the complexity of analyzing the data and undemanding the underlying mechanism. Despite progress, significant challenges persist, particularly in understanding the dynamic patterns of information diffusion, the long-term effects of algorithmic recommendations on network structure, and the role of AI agents in simulating user interactions within these systems.

Therefore, this Special Issue seeks state-of-the-art research on social network complexity, emphasizing theoretical, computational, and applied approaches. Topics include information spreading mechanisms, community structure change, algorithmic system dynamics, AI in social network models, and novel methodologies for complex network analysis. Contributions are encouraged to address emerging challenges in algorithm-driven social systems or propose innovative frameworks.

Prof. Dr. Zi-Ke Zhang
Dr. Junming Huang
Dr. Xiaoke Xu
Dr. Quanhui Liu
Guest Editors

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. Entropy is an international peer-reviewed open access monthly 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

  • social networks
  • social media
  • network structure dynamics
  • echo chambers
  • collective behavior
  • AI in social networks
  • information diffusion

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Published Papers (4 papers)

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Research

36 pages, 4216 KiB  
Article
Research on the Tail Risk Spillover Effect of Cryptocurrencies and Energy Market Based on Complex Network
by Xiao-Li Gong and Xue-Ting Wang
Entropy 2025, 27(7), 704; https://doi.org/10.3390/e27070704 - 30 Jun 2025
Viewed by 367
Abstract
As the relationship between cryptocurrency mining activities and electricity consumption becomes increasingly close, the risk spillover effect is steadily drawing a lot of attention to the energy and cryptocurrency markets. For the purpose of studying the risk contagion between the cryptocurrency and energy [...] Read more.
As the relationship between cryptocurrency mining activities and electricity consumption becomes increasingly close, the risk spillover effect is steadily drawing a lot of attention to the energy and cryptocurrency markets. For the purpose of studying the risk contagion between the cryptocurrency and energy market, this paper constructs a risk contagion network between cryptocurrency and China’s energy market using complex network methods. The tail risk spillover effects under various time and frequency domains were captured by the spillover index, which was assessed by the leptokurtic quantile vector autoregression (QVAR) model. Considering the spatial heterogeneity of energy companies, the spatial Durbin model was used to explore the impact mechanism of risk spillovers. The research showed that the framework of this paper more accurately reflects the tail risk spillover effect between China’s energy market and cryptocurrency market under various shock scales, with the extreme state experiencing a much higher spillover effect than the normal state. Furthermore, this study found that the tail risk contagion between cryptocurrency and China’s energy market exhibits notable dynamic variation and cyclical features, and the long-term risk spillover effect is primarily responsible for the total spillover. At the same time, the study found that the company with the most significant spillover effect does not necessarily have the largest company size, and other factors, such as geographical location and business composition, need to be considered. Moreover, there are spatial spillover effects among listed energy companies, and the connectedness between cryptocurrency and the energy market network generates an obvious impact on risk spillover effects. The research conclusions have an important role in preventing cross-contagion of risks between cryptocurrency and the energy market. Full article
(This article belongs to the Special Issue Complexity of Social Networks)
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22 pages, 397 KiB  
Article
Echo Chambers and Homophily in the Diffusion of Risk Information on Social Media: The Case of Genetically Modified Organisms (GMOs)
by Xiaoxiao Cheng and Jianbin Jin
Entropy 2025, 27(7), 699; https://doi.org/10.3390/e27070699 - 29 Jun 2025
Viewed by 428
Abstract
This study investigates the mechanisms underlying the diffusion of risk information about genetically modified organisms (GMOs) on the Chinese social media platform Weibo. Drawing upon social contagion theory, we examine how endogenous and exogenous mechanisms shape users’ information-sharing behaviors. An analysis of 388,722 [...] Read more.
This study investigates the mechanisms underlying the diffusion of risk information about genetically modified organisms (GMOs) on the Chinese social media platform Weibo. Drawing upon social contagion theory, we examine how endogenous and exogenous mechanisms shape users’ information-sharing behaviors. An analysis of 388,722 reposts from 2444 original GMO risk-related texts enabled the construction of a comprehensive sharing network, with computational text-mining techniques employed to detect users’ attitudes toward GMOs. To bridge the gap between descriptive and inferential network analysis, we employ a Shannon entropy-based approach to quantify the uncertainty and concentration of attitudinal differences and similarities among sharing and non-sharing dyads, providing an information-theoretic foundation for understanding positional and differential homophily. The entropy-based analysis reveals that information-sharing ties are characterized by lower entropy in attitude differences, indicating greater attitudinal alignment among sharing users, especially among GMO opponents. Building on these findings, the Exponential Random Graph Model (ERGM) further demonstrates that both endogenous network mechanisms (reciprocity, preferential attachment, and triadic closure) and positional homophily influence GMO risk information sharing and dissemination. A key finding is the presence of a differential homophily effect, where GMO opponents exhibit stronger homophilic tendencies than non-opponents. Despite the prevalence of homophily, this paper uncovers substantial cross-attitude interactions, challenging simplistic notions of echo chambers in GMO risk communication. By integrating entropy and ERGM analyses, this study advances a more nuanced, information-theoretic understanding of how digital platforms mediate public perceptions and debates surrounding controversial socio-scientific issues, offering valuable implications for developing effective risk communication strategies in increasingly polarized online spaces. Full article
(This article belongs to the Special Issue Complexity of Social Networks)
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22 pages, 1467 KiB  
Article
DDML: Multi-Student Knowledge Distillation for Hate Speech
by Ze Liu, Zerui Shao, Haizhou Wang and Beibei Li
Entropy 2025, 27(4), 417; https://doi.org/10.3390/e27040417 - 11 Apr 2025
Viewed by 491
Abstract
Recent studies have shown that hate speech on social media negatively impacts users’ mental health and is a contributing factor to suicide attempts. On a broader scale, online hate speech can undermine social stability. With the continuous growth of the internet, the prevalence [...] Read more.
Recent studies have shown that hate speech on social media negatively impacts users’ mental health and is a contributing factor to suicide attempts. On a broader scale, online hate speech can undermine social stability. With the continuous growth of the internet, the prevalence of online hate speech is rising, making its detection an urgent issue. Recent advances in natural language processing, particularly with transformer-based models, have shown significant promise in hate speech detection. However, these models come with a large number of parameters, leading to high computational requirements and making them difficult to deploy on personal computers. To address these challenges, knowledge distillation offers a solution by training smaller student networks using larger teacher networks. Recognizing that learning also occurs through peer interactions, we propose a knowledge distillation method called Deep Distill–Mutual Learning (DDML). DDML employs one teacher network and two or more student networks. While the student networks benefit from the teacher’s knowledge, they also engage in mutual learning with each other. We trained numerous deep neural networks for hate speech detection based on DDML and demonstrated that these networks perform well across various datasets. We tested our method across ten languages and nine datasets. The results demonstrate that DDML enhances the performance of deep neural networks, achieving an average F1 score increase of 4.87% over the baseline. Full article
(This article belongs to the Special Issue Complexity of Social Networks)
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20 pages, 2113 KiB  
Article
Identifying Influential Nodes Based on Evidence Theory in Complex Network
by Fu Tan, Xiaolong Chen, Rui Chen, Ruijie Wang, Chi Huang and Shimin Cai
Entropy 2025, 27(4), 406; https://doi.org/10.3390/e27040406 - 10 Apr 2025
Viewed by 662
Abstract
Influential node identification is an important and hot topic in the field of complex network science. Classical algorithms for identifying influential nodes are typically based on a single attribute of nodes or the simple fusion of a few attributes. However, these methods perform [...] Read more.
Influential node identification is an important and hot topic in the field of complex network science. Classical algorithms for identifying influential nodes are typically based on a single attribute of nodes or the simple fusion of a few attributes. However, these methods perform poorly in real networks with high complexity and diversity. To address this issue, a new method based on the Dempster–Shafer (DS) evidence theory is proposed in this paper, which improves the efficiency of identifying influential nodes through the following three aspects. Firstly, Dempster–Shafer evidence theory quantifies uncertainty through its basic belief assignment function and combines evidence from different information sources, enabling it to effectively handle uncertainty. Secondly, Dempster–Shafer evidence theory processes conflicting evidence using Dempster’s rule of combination, enhancing the reliability of decision-making. Lastly, in complex networks, information may come from multiple dimensions, and the Dempster–Shafer theory can effectively integrate this multidimensional information. To verify the effectiveness of the proposed method, extensive experiments are conducted on real-world complex networks. The results show that, compared to the other algorithms, attacking the influential nodes identified by the DS method is more likely to lead to the disintegration of the network, which indicates that the DS method is more effective for identifying the key nodes in the network. To further validate the reliability of the proposed algorithm, we use the visibility graph algorithm to convert the GBP futures time series into a complex network and then rank the nodes in the network using the DS method. The results show that the top-ranked nodes correspond to the peaks and troughs of the time series, which represents the key turning points in price changes. By conducting an in-depth analysis, investors can uncover major events that influence price trends, once again confirming the effectiveness of the algorithm. Full article
(This article belongs to the Special Issue Complexity of Social Networks)
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