ESTIMATING MODULARITY BOUNDS FOR HOMOPHILIC SCALE-FREE NETWORKS

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.