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Entropy
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Spreading Dynamics in Complex Networks
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Spreading Dynamics in Complex Networks

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

Deadline for manuscript submissions: 31 October 2025 | Viewed by 4822

Special Issue Editor

Prof. Dr. Lazaros Gallos

E-Mail Website
Guest Editor
DIMACS, The Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, Piscataway, NJ 08854-8018, USA
Interests: complex networks; epidemiology models; social networks; percolation; phase transitions

Special Issue Information

Dear Colleagues,

Complex networks have emerged as a powerful tool which has helped the research community understand how simple interactions can evolve into intricate large-scale systems with unforeseen properties. These networks provide the substrate that facilitates dynamical processes. The network topology can be critical to predicting the evolution of these processes and multiple new phenomena have been reported, compared to fully mixed models which ignore the network structure. This approach has enabled the study of numerous spreading phenomena with real-world implications and universally applicable principles. Universal features have been found in diverse systems, such as in the study of infectious diseases, computer viruses, information and misinformation, spreading belief propagation, and others. This Special Issue seeks to deepen our understanding of any type of spreading processes through networks from a holistic perspective, ranging from abstract models to analysis of real-world situations. Papers reporting theoretical results, data analysis, or computational modeling, as well as methodology papers are all welcome. Of particular interest is the potential of artificial intelligence models to transform our ability to analyze spreading processes.

Prof. Dr. Lazaros Gallos
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. 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

  • epidemic spreading
  • network science
  • network dynamics
  • information spreading
  • social network analysis
  • computational modeling
  • infectious disease modeling
  • percolation theory
  • machine learning in complex networks

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Published Papers (5 papers)

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Research

20 pages, 3634 KiB  
Article
LOMDP: Maximizing Desired Opinions in Social Networks by Considering User Expression Intentions
by Xuan Wang, Bin Wu and Tong Wu
Entropy 2025, 27(4), 360; https://doi.org/10.3390/e27040360 - 29 Mar 2025
Viewed by 202
Abstract
To address the problem of maximizing desired opinions in social networks, we present the Limited Opinion Maximization with Dynamic Propagation Optimization framework, which is grounded in information entropy theory. Innovatively, we introduce the concept of node expression capacity, which quantifies the uncertainty of [...] Read more.
To address the problem of maximizing desired opinions in social networks, we present the Limited Opinion Maximization with Dynamic Propagation Optimization framework, which is grounded in information entropy theory. Innovatively, we introduce the concept of node expression capacity, which quantifies the uncertainty of users’ expression intentions via entropy and effectively identifies the impact of silent nodes on the propagation process. Based on this, in terms of seed node selection, we develop the Limited Opinion Maximization algorithm for multi-stage seed selection, which dynamically optimizes the seed distribution among communities through a multi-stage seeding approach. In terms of node opinion changes, we establish the LODP dynamic opinion propagation model, reconstructing the node opinion update mechanism and explicitly modeling the entropy-increasing effect of silent nodes on the information propagation path. The experimental results on four datasets show that LOMDP outperforms six baseline algorithms. Our research effectively resolves the problem of maximizing desired opinions and offers insights into the dynamics of information propagation in social networks from the perspective of entropy and information theory. Full article
(This article belongs to the Special Issue Spreading Dynamics in Complex Networks)
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17 pages, 771 KiB  
Article
Multilevel Context Learning with Large Language Models for Text-Attributed Graphs on Social Networks
by Xiaokang Cai, Ruoyuan Gong and Hao Jiang
Entropy 2025, 27(3), 286; https://doi.org/10.3390/e27030286 - 10 Mar 2025
Viewed by 565
Abstract
There are complex graph structures and rich textual information on social networks. Text provides important information for various tasks, while graph structures offer multilevel context for the semantics of the text. Contemporary researchers tend to represent these kinds of data by text-attributed graphs [...] Read more.
There are complex graph structures and rich textual information on social networks. Text provides important information for various tasks, while graph structures offer multilevel context for the semantics of the text. Contemporary researchers tend to represent these kinds of data by text-attributed graphs (TAGs). Most TAG-based representation learning methods focus on designing frameworks that convey graph structures to large language models (LLMs) to generate semantic embeddings for downstream graph neural networks (GNNs). However, these methods only provide text attributes for nodes, which fails to capture the multilevel context and leads to the loss of valuable information. To tackle this issue, we introduce the Multilevel Context Learner (MCL) model, which leverages multilevel context on social networks to enhance LLMs’ semantic embedding capabilities. We model the social network as a multilevel context textual-edge graph (MC-TEG), effectively capturing both graph structure and semantic relationships. Our MCL model leverages the reasoning capabilities of LLMs to generate semantic embeddings by integrating these multilevel contexts. The tailored bidirectional dynamic graph attention layers are introduced to further distinguish the weight information. Experimental evaluations on six real social network datasets show that the MCL model consistently outperforms all baseline models. Specifically, the MCL model achieves prediction accuracies of 77.98%, 77.63%, 74.61%, 76.40%, 72.89%, and 73.40%, with absolute improvements of 9.04%, 9.19%, 11.05%, 7.24%, 6.11%, and 9.87% over the next best models. These results demonstrate the effectiveness of the proposed MCL model. Full article
(This article belongs to the Special Issue Spreading Dynamics in Complex Networks)
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11 pages, 695 KiB  
Article
Persistent Homology Combined with Machine Learning for Social Network Activity Analysis
by Zhijian Zhang, Yuqing Sun, Yayun Liu, Lin Jiang and Zhengmi Li
Entropy 2025, 27(1), 19; https://doi.org/10.3390/e27010019 - 30 Dec 2024
Viewed by 927
Abstract
Currently, the rapid development of social media enables people to communicate more and more frequently in the network. Classifying user activities in social networks helps to better understand user behavior in social networks. This paper first creates an ego network for each user, [...] Read more.
Currently, the rapid development of social media enables people to communicate more and more frequently in the network. Classifying user activities in social networks helps to better understand user behavior in social networks. This paper first creates an ego network for each user, encodes the higher-order topological features of the ego network as persistence diagrams using persistence homology, and computes the persistence entropy. Then, based on the persistence entropy, this paper defines the Norm Entropy-NE(X) to represent the complexity of the topological features of the ego network, a larger NE(X) indicates a higher topological complexity, i.e., the higher the activity of the nodes, thus indicating the degree of activity of the nodes. The paper uses the extracted set of feature vectors to train the machine learning model to classify the users in the social network. Numerical experiments are conducted to evaluate the performance of clustering quality metrics such as profile coefficients. The results show that the proposed algorithm can effectively classify social network users into different groups, which provides a good foundation for further research and application. Full article
(This article belongs to the Special Issue Spreading Dynamics in Complex Networks)
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19 pages, 4252 KiB  
Article
Information Propagation in Hypergraph-Based Social Networks
by Hai-Bing Xiao, Feng Hu, Peng-Yue Li, Yu-Rong Song and Zi-Ke Zhang
Entropy 2024, 26(11), 957; https://doi.org/10.3390/e26110957 - 6 Nov 2024
Cited by 1 | Viewed by 1334
Abstract
Social networks, functioning as core platforms for modern information dissemination, manifest distinctive user clustering behaviors and state transition mechanisms, thereby presenting new challenges to traditional information propagation models. Based on hypergraph theory, this paper augments the traditional SEIR model by introducing a novel [...] Read more.
Social networks, functioning as core platforms for modern information dissemination, manifest distinctive user clustering behaviors and state transition mechanisms, thereby presenting new challenges to traditional information propagation models. Based on hypergraph theory, this paper augments the traditional SEIR model by introducing a novel hypernetwork information dissemination SSEIR model specifically designed for online social networks. This model accurately represents complex, multi-user, high-order interactions. It transforms the traditional single susceptible state (S) into active (Sa) and inactive (Si) states. Additionally, it enhances traditional information dissemination mechanisms through reaction process strategies (RP strategies) and formulates refined differential dynamical equations, effectively simulating the dissemination and diffusion processes in online social networks. Employing mean field theory, this paper conducts a comprehensive theoretical derivation of the dissemination mechanisms within the SSEIR model. The effectiveness of the model in various network structures was verified through simulation experiments, and its practicality was further validated by its application on real network datasets. The results show that the SSEIR model excels in data fitting and illustrating the internal mechanisms of information dissemination within hypernetwork structures, further clarifying the dynamic evolutionary patterns of information dissemination in online social hypernetworks. This study not only enriches the theoretical framework of information dissemination but also provides a scientific theoretical foundation for practical applications such as news dissemination, public opinion management, and rumor monitoring in online social networks. Full article
(This article belongs to the Special Issue Spreading Dynamics in Complex Networks)
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18 pages, 4032 KiB  
Article
Synergistic Integration of Local and Global Information for Critical Edge Identification
by Na Zhao, Ting Luo, Hao Wang, Shuang-Ping Yang, Ni-Fei Xiong, Ming Jing and Jian Wang
Entropy 2024, 26(11), 933; https://doi.org/10.3390/e26110933 - 31 Oct 2024
Viewed by 848
Abstract
Identifying critical edges in complex networks is a fundamental challenge in the study of complex networks. Traditional approaches tend to rely solely on either global information or local information. However, this dependence on a single information source fails to capture the multi-layered complexity [...] Read more.
Identifying critical edges in complex networks is a fundamental challenge in the study of complex networks. Traditional approaches tend to rely solely on either global information or local information. However, this dependence on a single information source fails to capture the multi-layered complexity of critical edges, often resulting in incomplete or inaccurate identification. Therefore, it is essential to develop a method that integrates multiple sources of information to enhance critical edge identification and provide a deeper understanding and optimization of the structure and function of complex networks. In this paper, we introduce a Global–Local Hybrid Centrality method which integrates a second-order neighborhood index, a first-order neighborhood index, and an edge betweenness index, thus combining both local and global perspectives. We further employ the edge percolation process to evaluate the significance of edges in maintaining network connectivity. Experimental results on various real-world complex network datasets demonstrate that the proposed method significantly improves the accuracy of critical edge identification, providing theoretical and methodological support for the analysis and optimization of complex networks. Full article
(This article belongs to the Special Issue Spreading Dynamics in Complex Networks)
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