Heterogeneity of social network based on degree sequence and community

Abstract

As we know, the scale-free property of networks implies that there are a great deal of nodes with low degree and a few with high degree in networks. In this paper, we mainly stick to the analysis of the heterogeneity of social networks. Heterogeneity measure of degree sequence based on Laplacian centrality (HLC) and degree ratio (HDR) and local neighborhood (HLN) are presented. Furthermore, heterogeneities of community based on the size, edge abundant degree and density of community are explored, respectively. The heterogeneity measures of community are empirically analyzed in the real-world network in terms of these three indices, i.e., size, edge abundant degree and density of community.