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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Chala, Larysa
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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ESTIMATING MODULARITY BOUNDS FOR HOMOPHILIC SCALE-FREE NETWORKS Shergin, Vadim; Udovenko, Serhii; Miroshnychenko, Tetiana; Chala, Larysa; Dorokhov, Oleksandr
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0829-0840

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.
Co-Authors Dorokhov, Oleksandr Miroshnychenko, Tetiana Shergin, Vadim Udovenko, Serhii