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Detection of communities by modularity matrix | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 4، دوره 10، شماره 4، اسفند 2025، صفحه 359-374 اصل مقاله (768.47 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.11684.1112 | ||
| نویسندگان | ||
| Akram Hosseini1؛ Gholamhosein Fath-Tabar* 1؛ Hossein Shabani2 | ||
| 1Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran | ||
| 2Faculty of Computer, Network and Communication , Imam Hossein Comprehensive University, Tehran, I. R. Iran | ||
| تاریخ دریافت: 07 بهمن 1403، تاریخ بازنگری: 23 اسفند 1403، تاریخ پذیرش: 01 اردیبهشت 1404 | ||
| چکیده | ||
| One of the most discussed topics in social networks is community detection. As these networks become more complex, spectral graph properties and graph-related structures are increasingly used for community detection. In this paper, we examine these properties of the modularity matrix, such as the eigenvalues of the modularity matrix structure of some specific graphs, modularity energy, and the Estrada modularity index. Additionally, we study the bounds for the energy and Estrada indices. Furthermore, considering the significant issue of estimating the number of communities in some community detection algorithms in networks, we focus on the modularity eigenvalues. | ||
| کلیدواژهها | ||
| Estrada index؛ eigenvalues؛ communities estimate؛ graph energy؛ modularity matrix | ||
| مراجع | ||
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