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Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS...
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Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025

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

Deadline for manuscript submissions: closed (31 May 2026) | Viewed by 4908

Editor

Prof. Dr. Hocine Cherifi

E-Mail Website
Guest Editor
Carnot Interdisciplinary Laboratory of Burgundy (ICB) UMR 6303 CNRS, University of Burgundy, 21000 Dijon, France
Interests: signal and image processing; computer vision; data compression; complex systems; data science; complex network
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since 2012, the International Conference on Complex Networks and Their Applications (COMPLEX NETWORKS) has brought together researchers from different scientific communities working on areas related to network science. The fourteenth edition of this annual event will be held from 9 to 11 December 2025.

Authors of selected papers from the conference will be invited to submit extended versions of their original papers and contributions under the conference topics. They will reflect the latest problems, advances, and diversity within the network science community. New papers that are closely related to the conference themes are also welcome.

Topics of interest include, but are not limited to, the following:

  • structural network measures;
  • community structure;
  • link analysis and ranking;
  • motif discovery in complex networks;
  • network models;
  • diffusion and epidemics;
  • temporal networks;
  • multilayer networks;
  • dynamics on/of networks;
  • synchronization in networks;
  • resilience and robustness of networks;
  • controlling networks;
  • reputation, influence, and trust;
  • mobility;
  • networks in finance and economics;
  • ecological networks and food webs;
  • earth science applications;
  • biological networks;
  • brain networks;
  • urban systems and networks;
  • network medicine;
  • machine learning and networks

Prof. Dr. Hocine Cherifi
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

  • structural network measures
  • community structure
  • link analysis and ranking
  • motif discovery in complex networks
  • network models
  • diffusion and epidemics
  • temporal networks
  • multilayer networks
  • dynamics on/of networks
  • synchronization in networks
  • resilience and robustness of networks
  • controlling networks
  • reputation, influence, and trust
  • mobility
  • networks in finance and economics
  • ecological networks and food webs
  • earth science applications
  • biological networks
  • brain networks
  • urban systems and networks
  • network medicine
  • machine learning and networks

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (7 papers)

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Research

25 pages, 3094 KB  
Article
Deep Graph Clustering Framework Based on Confidence-Guided Graph Enhancement and Dual-Negative Sample Contrastive Learning
by Qiuming Wang, Sheng Zhang, Bing Wu, Jiangnan Zhou, Chennan Wu, Yirong Zeng, Ka Sun and Chang Liu
Entropy 2026, 28(7), 763; https://doi.org/10.3390/e28070763 - 3 Jul 2026
Viewed by 200
Abstract
Attributed graph clustering partitions nodes in an unsupervised manner by leveraging graph topology and node attributes. Existing deep methods face challenges including local structural bias, high noise in unsupervised graph editing, and insufficient discriminative ability for hard samples. To address these issues, we [...] Read more.
Attributed graph clustering partitions nodes in an unsupervised manner by leveraging graph topology and node attributes. Existing deep methods face challenges including local structural bias, high noise in unsupervised graph editing, and insufficient discriminative ability for hard samples. To address these issues, we propose a deep graph clustering framework based on confidence-guided graph enhancement and dual-negative sample contrastive learning (CGEN). CGEN constructs a local–global dual-view representation learning module to fuse local neighborhood attributes with high-order global topological information. It then utilizes a confidence-guided conservative graph editing mechanism that integrates multiple constraints, specifically feature similarity, intra-cluster consistency, multi-view consistency, and pairwise node confidence, using a progressive update strategy for stable structural optimization. Furthermore, a dual-negative sample contrastive learning strategy dynamically adjusts the weights of attribute-confused and inter-cluster-confused negative samples to enhance discriminative ability near adjacent cluster boundaries. Extensive experiments on four benchmark datasets demonstrate that CGEN achieves highly competitive performance, outperforming the majority of state-of-the-art methods across core clustering metrics, thereby validating its effectiveness in addressing local structural bias, graph editing noise, and hard sample discriminative limitations. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
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23 pages, 1750 KB  
Article
SAF: A Spectral-Adaptive Fusion Algorithm for Link Prediction in Complex Networks
by Wen Liang, Chunyu Yang, Qiwei Liu, Wenbo Zhang and Hongliang Wang
Entropy 2026, 28(7), 741; https://doi.org/10.3390/e28070741 - 1 Jul 2026
Viewed by 198
Abstract
Accurate prediction of missing or potential links is crucial for understanding complex network dynamics and supporting applications such as social recommendation and infrastructure planning. To effectively exploit both global and local structural information, this study proposes a spectral-adaptive fusion (SAF) algorithm. SAF first [...] Read more.
Accurate prediction of missing or potential links is crucial for understanding complex network dynamics and supporting applications such as social recommendation and infrastructure planning. To effectively exploit both global and local structural information, this study proposes a spectral-adaptive fusion (SAF) algorithm. SAF first constructs a spectral embedding matrix by retaining a subset of spectral components, from which a row-column normalized matrix and a Gaussian kernel matrix are derived. These matrices are then adaptively fused to produce link scores, using a common-neighbor-based mechanism that dynamically balances their contributions, capturing both local and global network features while mitigating the influence of highly central nodes. Energy retention and spectral gap analyses set the truncated ratio to 5%, resulting in an average runtime reduction of 71.0% across eight datasets. Under the AUC index, SAF achieves an average relative improvement of 2.22% over advanced graph neural network methods and 10.65% over matrix factorization approaches. Importantly, even at low training ratios, SAF maintains AUPR values above 0.91 on four networks and exhibits stable performance on recall, confirming its robustness and effectiveness for link prediction. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
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21 pages, 2018 KB  
Article
S2-HGNN: Scale-Aware Hypergraph Node Classification with Spectral Inductive Bias
by Jiangnan Zhou, Sheng Zhang, Bing Wu, Qiuming Wang, Chennan Wu, Ziqiang Luo, Ka Sun and Hongmei Mao
Entropy 2026, 28(6), 592; https://doi.org/10.3390/e28060592 - 26 May 2026
Viewed by 213
Abstract
Existing methods for hypergraph node classification usually rely on local message passing and use a unified strategy for topological modeling across hyperedges of different sizes. However, they have two limitations in semi-supervised settings. First, representation learning mainly depends on local neighborhoods, making it [...] Read more.
Existing methods for hypergraph node classification usually rely on local message passing and use a unified strategy for topological modeling across hyperedges of different sizes. However, they have two limitations in semi-supervised settings. First, representation learning mainly depends on local neighborhoods, making it difficult to incorporate global topological information. Second, a unified structural modeling strategy cannot effectively handle both small and large hyperedges. Small hyperedges require modeling fine-grained local relations, while large hyperedges need sparse group-level structure. To address these issues, we propose S2-HGNN, a scale-aware hypergraph node classification framework with spectral inductive bias for semi-supervised learning. S2-HGNN first injects global topological information into the input features using complementary hypergraph spectral operators. It then constructs different auxiliary topologies based on hyperedge size. For small hyperedges, it uses Top-k constrained clique expansion to preserve representative local relations. For large hyperedges, it uses star expansion to reduce redundant connections while preserving sparse group-level structure. Finally, node representations are jointly learned from the original hypergraph backbone and the two auxiliary branches, and final predictions are obtained through node-level adaptive fusion. Experiments on multiple public datasets show that the proposed method consistently outperforms strong baselines and exhibits superior robustness under feature perturbations. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
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28 pages, 13989 KB  
Article
Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks
by Mats Bierwirth and Johannes Lengler
Entropy 2026, 28(4), 401; https://doi.org/10.3390/e28040401 - 2 Apr 2026
Viewed by 502
Abstract
We investigate majority-vote opinion dynamics on Geometric Inhomogeneous Random Graphs (GIRGs), a powerful model for spatial complex networks. In contrast to classic coarsening dynamics, where a single opinion typically achieves global consensus, our simulations reveal that sufficiently large, localized opinion domains do not [...] Read more.
We investigate majority-vote opinion dynamics on Geometric Inhomogeneous Random Graphs (GIRGs), a powerful model for spatial complex networks. In contrast to classic coarsening dynamics, where a single opinion typically achieves global consensus, our simulations reveal that sufficiently large, localized opinion domains do not disappear. Instead, they stabilize, leading to a persistent coexistence of competing opinions. To understand the mechanism behind this arrested coarsening, we develop and analyze a tractable mean-field model of the interface between two opinion domains. Our main theoretical result rigorously establishes the existence of a stable, non-trivial limiting distribution for the interface profile in a mean-field analysis. This demonstrates that the boundary between opinions is stationary, providing a mathematical explanation for how complex network geometry can support robust opinion diversity in social systems. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
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25 pages, 2523 KB  
Article
Link Prediction in Heterogeneous Information Networks: Improved Hypergraph Convolution with Adaptive Soft Voting
by Sheng Zhang, Yuyuan Huang, Ziqiang Luo, Jiangnan Zhou, Bing Wu, Ka Sun and Hongmei Mao
Entropy 2026, 28(2), 230; https://doi.org/10.3390/e28020230 - 16 Feb 2026
Cited by 1 | Viewed by 761
Abstract
Complex real-world systems are often modeled as heterogeneous information networks with diverse node and relation types, bringing new opportunities and challenges to link prediction. Traditional methods based on similarity or meta-paths fail to fully capture high-order structures and semantics, while existing hypergraph-based models [...] Read more.
Complex real-world systems are often modeled as heterogeneous information networks with diverse node and relation types, bringing new opportunities and challenges to link prediction. Traditional methods based on similarity or meta-paths fail to fully capture high-order structures and semantics, while existing hypergraph-based models homogenize all high-order information without considering their importance differences, diluting core associations with redundant noise and limiting prediction accuracy. Given these issues, we propose the VE-HGCN, a link prediction model for HINs that fuses hypergraph convolution with soft-voting ensemble strategy. The model first constructs multiple heterogeneous hypergraphs from HINs via network frequent subgraph pattern extraction, then leverages hypergraph convolution for node representation learning, and finally employs a soft-voting ensemble strategy to fuse multi-model prediction results. Extensive experiments on four public HIN datasets show that the VE-HGCN outperforms seven mainstream baseline models, thereby validating the effectiveness of the proposed method. This study offers a new perspective for link prediction in HINs and exhibits good generality and practicality, providing a feasible reference for addressing high-order information utilization issues in complex heterogeneous network analysis. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
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21 pages, 1514 KB  
Article
TaCD: Team-Aware Community Detection Based on Multi-View Modularity
by Chengzhou Fu, Feiyi Tang, Lingzhi Hu, Chengzhe Yuan and Ronghua Lin
Entropy 2026, 28(1), 21; https://doi.org/10.3390/e28010021 - 24 Dec 2025
Viewed by 656
Abstract
Community detection in social networks is one of the most important topics of network science. Researchers have developed numerous methods from various perspectives. However, the existing methods often overlook the team information encoded as a special type of user relation in the social [...] Read more.
Community detection in social networks is one of the most important topics of network science. Researchers have developed numerous methods from various perspectives. However, the existing methods often overlook the team information encoded as a special type of user relation in the social network, which plays an important role in community formation and evolution. In this paper, we propose a novel community detection algorithm called Team-aware Community Detection (TaCD). Our model constructs a multi-view network by encoding the user interaction information as the user view and the team information as the team view. To measure the consistency across the two views, we use the Jaccard similarity to establish a cross-view coupling. Based on the constructed 2-view network, we use multi-view modularity to discover team-aware community structure, and solve the optimization problem using the well-known Generalized Louvain approach. Another contribution of this paper is the collection of a new SCHOLAT dataset, which consists of several social networks with team information and is publicly available for testing purposes. Our experimental results on several SCHOLAT networks with team information demonstrate that TaCD outperforms the existing community detection algorithms. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
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34 pages, 2015 KB  
Article
Exploring the Digital Economy Innovation in the Yangtze River Delta: A Perspective of Complex Networks
by Luyun Sun, Pan Zhao and Benda Zhou
Entropy 2025, 27(12), 1241; https://doi.org/10.3390/e27121241 - 8 Dec 2025
Viewed by 1203
Abstract
As a major economic engine of China, the Yangtze River Delta (YRD) region is pivotal in driving innovation across the scientific, technological, and digital economies. This study constructs the spatial associative network for digital economy innovation by treating 41 cities as nodes and [...] Read more.
As a major economic engine of China, the Yangtze River Delta (YRD) region is pivotal in driving innovation across the scientific, technological, and digital economies. This study constructs the spatial associative network for digital economy innovation by treating 41 cities as nodes and applying a gravity model adjusted for institutional distance. Subsequently, the structural characteristics of the spatial associative network and their effects were empirically explored by using complex network analysis and regression models. The findings indicate that: (1) The linkages in digital economy innovation among cities are becoming increasingly closer, and the network structure exhibits an annual increasing trend in density, connectivity, and efficiency, while hierarchy decreases; (2) The examination of network node characteristics discloses that different cities possess diverse capabilities in terms of resource aggregation, regulation, and communication. The block model analysis further categorizes the cities into four functional groups. Among them, Block I (including cities like Shanghai, Nanjing, and Hangzhou) holds the “primary” status and acts as the “core city” for digital economy innovation; (3) The attributes of the spatial associative network have a remarkable effect on both the degree of digital economy innovation and the variations among cities. Full article
(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
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