Expansion properties of large social graphs

Abstract

Social network analysis has become an extremely popular research area, where the main focus is the understanding of networks’ structure. In this paper, we study the expansibility of large social graphs, a structural property based on the notion of expander graphs (i.e. sparse graphs with strong connectivity properties). It is widely believed that social networks have poor expansion properties, due to their community-based organization. Moreover, this was experimentally confirmed on small scale networks and it is considered as a global property of social networks (independent of the graph’s size) in many applications. What really happens in large scale social graphs? To address this question, we measure the expansion properties of several large scale social graphs using the measure of subgraph centrality. Our findings show a clear difference on the expansibility between small and large scale social networks, and thus structural differences. Our observations could be utilized in a range of applications which are based on social graphs’ structure.