Characterising and modelling social networks with overlapping communities

Abstract

Social networks, as well as many other real-world networks, exhibit overlapping community structure. Affiliation networks, as a large portion of social networks, consist of cooperative individuals: two individuals are connected by a link if they belong to the same organisations, such as companies, research groups and hobby clubs. Affiliation networks naturally contain many fully connected communities/groups. In this paper, we characterise the structure of the real-world affiliation networks, and propose a growing hypergraph model with preferential attachment for affiliation networks, which reproduces the clique structure of affiliation networks. By comparing computational results of our model with measurements of the real-world affiliation networks of ArXiv co-authorship, IMDB actors collaboration and SourceForge collaboration, we show that our model captures the fundamental properties including the power-law distributions of group size, group degree, overlapping depth, individual degree and interest-sharing number of real-world affiliation networks, and reproduces the properties of high clustering, assortative mixing and short average path length of real-world affiliation networks.