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Mathematics
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Modeling and Data Analysis of Complex Networks
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Modeling and Data Analysis of Complex Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 1664

Special Issue Editor

Dr. Hongbin Pei

E-Mail Website
Guest Editor
School of Cyber Science and Engineering, Xi’an Jiaotong University, Xi'an 710049, China
Interests: graph machine learning and graph mining; geometric deep learning; complex networks

Special Issue Information

Dear Colleagues,

Complex networks are ubiquitous in the real world, with social networks, transportation systems, protein interactions, power grids, computer networks, and the world wide web being examples of such. With a long history of study, significant developments have positioned network science as a key research focus in multiple scientific fields. Research here drives advancements across diverse applications, including in public opinion analysis, cybersecurity, drug discovery, and intelligent transportation.

In recent years, the use of deep learning with complex networks has gained significant attention, with Graph Neural Networks (GNNs) emerging as a powerful method for graph representation learning. Their ability to capture intricate relational structures and high-order dependencies within complex networks has made them essential for advancing both theoretical research and real-world applications.

This Special Issue, “Modeling and Data Analysis of Complex Networks”, aims to showcase recent advances in modeling, analyzing, and applying complex network across scientific and engineering domains. We invite contributions that introduce novel methodologies, computational techniques, and real-world applications that enhance our understanding of complex networks. Topics of interest include, but are not limited to, the following:

  • Network structure and property analysis;
  • Higher-order interaction analysis;
  • Graph representation learning;
  • Network dynamics;
  • Community detection;
  • Anomaly detection in networks;
  • Robustness and resilience;
  • Real-world applications.

Dr. Hongbin Pei
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 networks
  • graph machine learning
  • graph neural networks
  • graph representation learning
  • graph mining
  • geometric deep learning
  • social networks
  • network science
  • network structure
  • network dynamics
  • graph-structured data
  • deep learning
  • machine learning
  • graph data mining
  • data-driven complex system modeling

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

Published Papers (3 papers)

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24 pages, 443 KB  
Article
Consistent Markov Edge Processes and Random Graphs
by Donatas Surgailis
Mathematics 2025, 13(21), 3368; https://doi.org/10.3390/math13213368 - 22 Oct 2025
Viewed by 129
Abstract
We discuss Markov edge processes {Ye;e∈E} defined on edges of a directed acyclic graph (V,E) with the consistency property [...] Read more.
We discuss Markov edge processes {Ye;e∈E} defined on edges of a directed acyclic graph (V,E) with the consistency property PE′(Ye;e∈E′)=PE(Ye;e∈E′) for a large class of subgraphs (V′,E′) of (V,E) obtained through a mesh dismantling algorithm. The probability distribution PE of such edge process is a discrete version of consistent polygonal Markov graphs. The class of Markov edge processes is related to the class of Bayesian networks and may be of interest to causal inference and decision theory. On regular ν-dimensional lattices, consistent Markov edge processes have similar properties to Pickard random fields on Z2, representing a far-reaching extension of the latter class. A particular case of binary consistent edge process on Z3 was disclosed by Arak in a private communication. We prove that the symmetric binary Pickard model generates the Arak model on Z2 as a contour model. Full article
(This article belongs to the Special Issue Modeling and Data Analysis of Complex Networks)
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23 pages, 2056 KB  
Article
Modeling the Evolution of AI Identity Using Structural Features and Temporal Role Dynamics in Complex Networks
by Yahui Lu, Raihanah M. M. and Ravichandran Vengadasamy
Mathematics 2025, 13(20), 3315; https://doi.org/10.3390/math13203315 - 17 Oct 2025
Viewed by 260
Abstract
In increasingly networked environments, artificial agents are required to operate not with fixed roles but with identities that adapt, evolve, and emerge through interaction. Traditional identity modeling approaches, whether symbolic or statistical, fail to capture this dynamic, relational nature. This paper proposes a [...] Read more.
In increasingly networked environments, artificial agents are required to operate not with fixed roles but with identities that adapt, evolve, and emerge through interaction. Traditional identity modeling approaches, whether symbolic or statistical, fail to capture this dynamic, relational nature. This paper proposes a network-based framework for constructing and analyzing AI identity by modeling interaction, representation, and emergence within complex networks. The goal is to uncover how agent identity can be inferred and explained through structural roles, temporal behaviors, and community dynamics. The approach begins by transforming raw data from three benchmark domain, Reddit, the Interaction Network dataset, and AMine, into temporal interaction graphs. These graphs are structurally enriched via motif extraction, centrality scoring, and community detection. Graph Neural Networks (GNNs), including GCNs, GATs, and GraphSAGE, are applied to learn identity embeddings across time slices. Extensive evaluations include identity coherence, role classification accuracy, and temporal embedding consistency. Ablation studies assess the contribution of motif and temporal layers. The proposed model achieves strong performance across all metrics. On the AMiner dataset, identity coherence reaches 0.854, with a role classification accuracy of 80.2%. GAT demonstrates the highest temporal consistency and resilience to noise. Role trajectories and motif patterns confirm the emergence of stable and transient identities over time. The results validate the fact that the framework is not only associated with healthy quantitative performance but also offers information on behavioral development. The model will be expanded with semantic representations and be more concerned with ethical considerations, such as privacy, fairness, and transparency, to make identity modeling in artificial intelligence systems responsible and trustworthy. Full article
(This article belongs to the Special Issue Modeling and Data Analysis of Complex Networks)
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22 pages, 4113 KB  
Article
PathGen-LLM: A Large Language Model for Dynamic Path Generation in Complex Transportation Networks
by Xun Li, Kai Xian, Huimin Wen, Shengguang Bai, Han Xu and Yun Yu
Mathematics 2025, 13(19), 3073; https://doi.org/10.3390/math13193073 - 24 Sep 2025
Viewed by 659
Abstract
Dynamic path generation in complex transportation networks is essential for intelligent transportation systems. Traditional methods, such as shortest path algorithms or heuristic-based models, often fail to capture real-world travel behaviors due to their reliance on simplified assumptions and limited ability to handle long-range [...] Read more.
Dynamic path generation in complex transportation networks is essential for intelligent transportation systems. Traditional methods, such as shortest path algorithms or heuristic-based models, often fail to capture real-world travel behaviors due to their reliance on simplified assumptions and limited ability to handle long-range dependencies or non-linear patterns. To address these limitations, we propose PathGen-LLM, a large language model (LLM) designed to learn spatial–temporal patterns from historical paths without requiring handcrafted features or graph-specific architectures. Exploiting the structural similarity between path sequences and natural language, PathGen-LLM converts spatiotemporal trajectories into text-formatted token sequences by encoding node IDs and timestamps. This enables the model to learn global dependencies and semantic relationships through self-supervised pretraining. The model integrates a hierarchical Transformer architecture with dynamic constraint decoding, which synchronizes spatial node transitions with temporal timestamps to ensure physically valid paths in large-scale road networks. Experimental results on real-world urban datasets demonstrate that PathGen-LLM outperforms baseline methods, particularly in long-distance path generation. By bridging sequence modeling and complex network analysis, PathGen-LLM offers a novel framework for intelligent transportation systems, highlighting the potential of LLMs to address challenges in large-scale, real-time network tasks. Full article
(This article belongs to the Special Issue Modeling and Data Analysis of Complex Networks)
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