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Mathematics
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Advances in the Research of Complex Network Algorithms
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Advances in the Research of Complex Network Algorithms

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1944

Special Issue Editor

Dr. Jianjia Wang

E-Mail Website
Guest Editor
School of Artificial Intelligence and Advanced Computing (AIAC), Xi'an Jiaotong-Liverpool University, Suzhou 215412, China
Interests: statistical and structural pattern recognition; complex networks; machine learning for graphs and networks; thermodynamic and quantum statistics; information theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The study of complex networks focuses on understanding the intricate relationships and patterns within interconnected systems. Statistical structural analysis plays a crucial role in this field, providing tools to quantify and interpret the global organization and properties of complex networks. This involves analyzing various network properties with the aim to identify patterns, quantify structural features, and develop models to explain the network's behavior. By applying statistical techniques, researchers can quantify these properties and test hypotheses about network formation and evolution. This analysis helps us understand how complex networks function, evolve, and influence various phenomena across diverse fields.

Dr. Jianjia Wang
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

  • models of complex networks
  • structural network properties and analysis
  • network statistical inference
  • machine learning with graphs
  • complex networks and information systems

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Published Papers (2 papers)

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Research

23 pages, 2566 KiB  
Article
Rootlets Hierarchical Principal Component Analysis for Revealing Nested Dependencies in Hierarchical Data
by Korey P. Wylie and Jason R. Tregellas
Mathematics 2025, 13(1), 72; https://doi.org/10.3390/math13010072 - 28 Dec 2024
Viewed by 621
Abstract
Hierarchical clustering analysis (HCA) is a widely used unsupervised learning method. Limitations of HCA, however, include imposing an artificial hierarchy onto non-hierarchical data and fixed two-way mergers at every level. To address this, the current work describes a novel rootlets hierarchical principal component [...] Read more.
Hierarchical clustering analysis (HCA) is a widely used unsupervised learning method. Limitations of HCA, however, include imposing an artificial hierarchy onto non-hierarchical data and fixed two-way mergers at every level. To address this, the current work describes a novel rootlets hierarchical principal component analysis (hPCA). This method extends typical hPCA using multivariate statistics to construct adaptive multiway mergers and Riemannian geometry to visualize nested dependencies. The rootlets hPCA algorithm and its projection onto the Poincaré disk are presented as examples of this extended framework. The algorithm constructs high-dimensional mergers using a single parameter, interpreted as a p-value. It decomposes a similarity matrix from GL(m, ℝ) using a sequence of rotations from SO(k), k << m. Analysis shows that the rootlets algorithm limits the number of distinct eigenvalues for any merger. Nested clusters of arbitrary size but equal correlations are constructed and merged using their leading principal components. The visualization method then maps elements of SO(k) onto a low-dimensional hyperbolic manifold, the Poincaré disk. Rootlets hPCA was validated using simulated datasets with known hierarchical structure, and a neuroimaging dataset with an unknown hierarchy. Experiments demonstrate that rootlets hPCA accurately reconstructs known hierarchies and, unlike HCA, does not impose a hierarchy on data. Full article
(This article belongs to the Special Issue Advances in the Research of Complex Network Algorithms)
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21 pages, 10545 KiB  
Article
New Random Walk Algorithm Based on Different Seed Nodes for Community Detection
by Jiansheng Cai, Wencong Li, Xiaodong Zhang and Jihui Wang
Mathematics 2024, 12(15), 2374; https://doi.org/10.3390/math12152374 - 30 Jul 2024
Viewed by 1012
Abstract
A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new [...] Read more.
A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new community detection algorithm (RWBS) based on different seed nodes which aims to understand the community structure of the network, which provides a new idea for the allocation of resources in the network. RWBS provides a new centrality metric (MC) to calculate node importance, which calculates the ranking of nodes as seed nodes. Furthermore, two algorithms are proposed for determining seed nodes on networks with and without ground truth, respectively. We set the number of steps for the random walk to six according to the six degrees of separation theory to reduce the running time of the algorithm. Since some traditional community detection algorithms may detect smaller communities, e.g., two nodes become one community, this may make the resource allocation unreasonable. Therefore, modularity (Q) is chosen as the optimization function to combine communities, which can improve the quality of detected communities. Final experimental results on real-world and synthetic networks show that the RWBS algorithm can effectively detect communities. Full article
(This article belongs to the Special Issue Advances in the Research of Complex Network Algorithms)
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