Modeling influence diffusion to uncover influence centrality and community structure in social networks

Node centrality and vertex similarity in network graph topology are two of the most fundamental and significant notions for network analysis. Defining meaningful and quantitatively precise measures of them, however, is nontrivial but an important challenge. In this paper, we base our centrality and similarity measures on the idea of influence of a node and exploit the implicit knowledge of influence-based connectivity encoded in the network graph topology. We arrive at a novel influence diffusion model, which builds egocentric influence rings and generates an influence vector for each node. It captures not only the total influence but also its distribution that each node spreads through the network. A Shared-Influence-Neighbor (SIN) similarity defined in this influence space gives rise to a new, meaningful and refined connectivity measure for the closeness of any pair of nodes. Using this influence diffusion model, we propose a novel influence centrality for influence analysis and an Influence-Guided Spherical K-means (IGSK) algorithm for community detection. Our approach not only differentiates the influence ranking in a more detailed manner but also effectively finds communities in both undirected/directed and unweighted/weighted networks. Furthermore, it can be easily adapted to the identification of overlapping communities and individual roles in each community. We demonstrate its superior performance with extensive tests on a set of real-world networks and synthetic benchmarks. © 2015, Springer-Verlag Wien.