Estimating Modularity Bounds for Homophilic Scale-Free Networks

21 March 2025 20:00

The next meeting of the seminar was held on March 21, 2025.

The seminar was reported by the assistant professor of the department, Sergey Grinyov; the topic of the report is “Estimating Modularity Bounds for Homophilic Scale-Free Networks”.

The report on this task estimates the modularity bounds for homophilic and scale-free networks. It is noted that the key property of homophilic networks is the tendency of nodes to connect with similar nodes that belong to the same community. Thus, homophily is a natural mechanism for community formation, that is, network structuring. One of the measures of network structuring is modularity. In homophilic networks, the degrees of node distribution can be scale-free and the distribution of community sizes. At the same time, the community can differ significantly in size, which leads to the sounding of real achievable modularity. The report demonstrates estimates of the modularity bounds of the network of the presented class. Mathematically rigorous estimates correspond to non-elementary functions, which complicates the practical application of such estimates. The obtained approximate estimates with high (0.005) accuracy for the most characteristic values ​​of the network parameters were demonstrated.

The report aroused the interest of the department’s teachers and the number of questions to which the speaker provided substantiated answers.