ESTIMATING MODULARITY BOUNDS FOR HOMOPHILIC SCALE-FREE NETWORKS

  • Vadim Shergin Artificial Intelligence Department, Faculty of Computer Science, Kharkiv National University of Radio Electronics, Ukraine https://orcid.org/0000-0002-4388-8180
  • Serhii Udovenko Department of Informatics and Computer Engineering, Educational and Scientific Institute of Information Technologies, Simon Kuznets Kharkiv National University of Economics, Ukraine https://orcid.org/0000-0001-5945-8647
  • Tetiana Miroshnychenko Artificial Intelligence Department, Faculty of Computer Science, Kharkiv National University of Radio Electronics, Ukraine https://orcid.org/0009-0006-0742-0528
  • Larysa Chala Artificial Intelligence Department, Faculty of Computer Science, Kharkiv National University of Radio Electronics, Ukraine https://orcid.org/0000-0002-9890-4790
  • Oleksandr Dorokhov Department of Public Economics and Policy, School of Economics and Business Administration, University of Tartu, Estonia https://orcid.org/0000-0002-0737-8714
DOI: https://doi.org/10.30598/barekengvol20iss1pp0829-0840
Keywords: Communities, Homophilic networks, Modularity boundaries, Network analysis, Scale-free networks

Abstract

The problem of estimating the modularity boundaries for networks that are both homophilic and scale-free is considered. The key property of homophilic networks is the tendency of nodes to link with similar nodes, i.e., belonging to the same community. Thus, homophily is a natural mechanism for community formation, i.e., network structuring. One of the measures of network structuring is modularity. In homophilic networks, not only can the distribution of node degrees be scale-free, but also the distribution of community sizes. In this case, communities can differ significantly in size, which leads to narrowing the achievable modularity boundaries. Estimates of the modularity boundaries of networks of the considered class are obtained. Mathematically strict estimates contain non-elementary functions, which complicates the practical application of such estimates. Approximate estimates with high (0.005) accuracy for the most characteristic values of network parameters are obtained.

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Published
2025-11-24
How to Cite
[1]
V. Shergin, S. Udovenko, T. Miroshnychenko, L. Chala, and O. Dorokhov, “ESTIMATING MODULARITY BOUNDS FOR HOMOPHILIC SCALE-FREE NETWORKS”, BAREKENG: J. Math. & App., vol. 20, no. 1, pp. 0829-0840, Nov. 2025.
Issue
Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2025 Vadim Shergin, Serhii Udovenko, Tetiana Miroshnychenko, Larysa Chala, Oleksandr Dorokhov

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