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Entropy
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Dynamics in Biological and Social Networks, Second Edition
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Dynamics in Biological and Social Networks, Second Edition

A Special Issue of Entropy (ISSN 1099-4300) belonging to the section "Complexity".

Deadline for manuscript submissions: closed (10 August 2026) | Viewed by 2213

Editor

Dr. Luiz Henrique Alves Monteiro

E-Mail Website
Guest Editor
1. Escola de Engenharia, Universidade Presbiteriana Mackenzie, São Paulo 01302-907, Brazil
2. Escola Politécnica, Universidade de São Paulo, São Paulo 05508-010, Brazil
Interests: complex networks; dynamical systems; epidemiology; game theory; social networks; synchronization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This is the second edition of the Special Issue titled "Dynamics in Biological and Social Networks". The first edition included seven high-quality papers and attracted widespread attention. Therefore, we decided to release a second edition to continue focusing on this research area.

The dynamics of biological and social systems result from the intricate interaction of many elements; hence, such systems are usually represented by complex networks. In fact, life depends on the activity of genes, neurons, and proteins; ecosystems rely on their biodiversity; and societies are affected by the spread of diseases, information, and opposing ideas. From an academic perspective, these subjects are translated into investigations on a wide range of topics, such as the following:

  • Chaotic behavior;
  • Epidemiology;
  • Gene regulatory networks;
  • Information flow;
  • Metabolic pathways;
  • Neuronal networks;
  • Online social media;
  • Opinion dynamics;
  • Population dynamics;
  • Protein–protein interaction;
  • Social network mining;

These investigations are based, for instance, on cellular automata, differential equations, game-theoretic models, multi-agent simulations, and network analysis. Thus, analytical and numerical techniques are employed to deepen our understanding of real-world phenomena.

Entropy measures have been proposed to quantify the amount of variability and the level of complexity found in a broad spectrum of networks. This Special Issue of Entropy is devoted to studies on the dynamics in biological and social networks. These studies should be carried out, at least partially, by drawing upon concepts from information theory. Submissions of original contributions and review articles are both welcome. The submitted manuscripts will be peer-reviewed and the authors will receive timely feedback.

Dr. Luiz Henrique Alves Monteiro
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • agent-based model
  • cellular automata
  • complex network
  • dynamical systems
  • entropy measures
  • game theory
  • social media
  • social network
  • systems biology

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Related Special Issue

Published Papers (4 papers)

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Research

26 pages, 1061 KB  
Article
Co-Opetitive Bridging Structure in Rumor Cascades: A Multilayer Overlapping Community Approach with Information-Theoretic Characterization
by Sijia Sun and Tian Liu
Entropy 2026, 28(9), 978; https://doi.org/10.3390/e28090978 - 2 Sep 2026
Viewed by 182
Abstract
Rumor events on social media generate opposing camps whose interaction structure is not captured by spreading models or content detectors. This study describes the camp and bridging structure of three rumor events on Sina Weibo, selected from confirmed cases published by the platform’s [...] Read more.
Rumor events on social media generate opposing camps whose interaction structure is not captured by spreading models or content detectors. This study describes the camp and bridging structure of three rumor events on Sina Weibo, selected from confirmed cases published by the platform’s rumor-refutation channel. Each event is represented as a multilayer interaction network built from repost, comment, and mention relations. Camps are detected by modularity-based community assignment, and overlap is measured through a fractional membership distribution over communities. Three information-theoretic quantities characterize the structure. In the three events, membership entropy separates committed users from bridging users. Structure-to-stance mutual information measures the alignment between interaction communities and text stance. Cross-layer mutual information measures the consistency of camps across interaction types. A co-opetition matrix of mean edge sentiment describes cooperation within camps and competition between camps and identifies alliance structure. In the three events, membership entropy is bimodal, structure-to-stance mutual information is positive and above a permutation null, and the co-opetition matrix has positive diagonal entries. The three events show three distinct temporal patterns, namely a persistent standoff, a hardening toward a single camp after an official correction, and a reversal with an alliance between two camps. The patterns are recovered under a look-ahead-free temporal scheme. In the three events, bridging users hold higher betweenness centrality than non-bridging users. The results describe cross-camp bridging structure in three rumor cascades and connect the structure to a co-opetition reading of camp relations. Full article
(This article belongs to the Special Issue Dynamics in Biological and Social Networks, Second Edition)
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14 pages, 350 KB  
Article
An Agent-Based Model of Cooperation and Competition in Organizational Systems
by D. S. Fonte and L. H. A. Monteiro
Entropy 2026, 28(9), 965; https://doi.org/10.3390/e28090965 - 29 Aug 2026
Viewed by 201
Abstract
This study proposes a game-theoretic agent-based model to investigate cooperation and competition in workplace environments. The iterated prisoner’s dilemma is implemented on a two-dimensional lattice, where agents interact locally and accumulate wealth over time. Two types of agents are considered: fixed probabilistic cooperators, [...] Read more.
This study proposes a game-theoretic agent-based model to investigate cooperation and competition in workplace environments. The iterated prisoner’s dilemma is implemented on a two-dimensional lattice, where agents interact locally and accumulate wealth over time. Two types of agents are considered: fixed probabilistic cooperators, who adopt a constant cooperation probability, and adaptive probabilistic cooperators, whose behavior depends on their accumulated wealth and reputation. Population composition and wealth distribution are quantified using Shannon entropy and the Gini coefficient. Numerical simulations show that fixed cooperators tend to predominate and accumulate higher average wealth. The simulations also show that increasing tolerance to defections raises average wealth and reduces inequality. In contrast, a higher cooperation probability increases wealth but may also amplify inequality. These results highlight the role of reputation and performance targets in shaping cooperation in organizational environments. Full article
(This article belongs to the Special Issue Dynamics in Biological and Social Networks, Second Edition)
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26 pages, 3934 KB  
Article
Modeling and Simulating Complex Conflict Management Using Reaction Networks
by Tomas Veloz, Dirk Bruin and Cedric De Coning
Entropy 2026, 28(7), 754; https://doi.org/10.3390/e28070754 - 1 Jul 2026
Viewed by 578
Abstract
Evidence suggests that protracted conflicts persist because several forms of socio-political organization run simultaneously on the same population, resources, and territory. Reading Service’s typology of bands, tribes, chiefdoms, and states not as evolutionary stages but as coexisting and superposed social organizations, we model [...] Read more.
Evidence suggests that protracted conflicts persist because several forms of socio-political organization run simultaneously on the same population, resources, and territory. Reading Service’s typology of bands, tribes, chiefdoms, and states not as evolutionary stages but as coexisting and superposed social organizations, we model conflict as a reaction network where each social form is a self-maintaining set of stocks—a chemical organization—and conflicts arise where competing productive logics between organizations generate stocks with negative connotation, such as grievances and displacement. Taking the Lake Chad Basin as inspiration, we build a ladder of progressively richer models arriving a mixed chiefdom–state configuration compatible with current views on the conflict. As the model complexifies, kinetic approaches become uninformative; we therefore develop complementary stoichiometric methods that are parameter-free and thus are far easier to measure and compute. These diagnostics reveal a structural bias toward conflict: transitions into conflict regimes are systematically richer than transitions out. We show how a dual chiefdom–state form acts as a conflict attractor within a closed conflict–peace loop that transits among documented different forms of organization. Conflict management then becomes the identification of the mechanisms that redirect rather than change the state of a self-sustaining organization—here, elite-surplus redistribution—and of the timescales at which such redirection is observable, turning intervention design into a structural rather than a parameter-tuning problem. Full article
(This article belongs to the Special Issue Dynamics in Biological and Social Networks, Second Edition)
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22 pages, 1269 KB  
Article
Mining the Collaborative Networks: A Machine Learning-Based Approach to Firm Innovation in the Digital Transformation Era
by Wenhao Zhou and Zhiwei Zhang
Entropy 2026, 28(3), 357; https://doi.org/10.3390/e28030357 - 22 Mar 2026
Cited by 1 | Viewed by 706
Abstract
Understanding how collaborative network structures and digital transformation jointly shape firm innovation has become a critical issue amid rapid technological change. Drawing on social network theory and a configurational perspective, this study investigates the nonlinear and interactive effects of collaborative network characteristics and [...] Read more.
Understanding how collaborative network structures and digital transformation jointly shape firm innovation has become a critical issue amid rapid technological change. Drawing on social network theory and a configurational perspective, this study investigates the nonlinear and interactive effects of collaborative network characteristics and digital transformation on firm innovation performance. Using patent data from Chinese listed manufacturing firms for the period between 2012 and 2022, inter-firm technological collaboration networks are constructed based on co-patenting relationships. A Classification and Regression Tree (CART) model is employed to uncover complex configurational patterns, complemented by regression-based robustness tests. The results reveal that innovation outcomes are not driven by single network attributes but by joint configurations of structural hole positions, centrality measures, and digital transformation. Among all factors, structural holes emerge as the most influential determinant. The findings further show that digital transformation interacts with network positions, generating multiple paths leading to high or low innovation performance. Model comparisons demonstrate that the CART approach outperforms traditional linear models in capturing nonlinear effects. This study contributes to the literature by highlighting the configurational logic of collaborative innovation and providing a machine learning-based framework for analyzing network–digital transformation interplay. Full article
(This article belongs to the Special Issue Dynamics in Biological and Social Networks, Second Edition)
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