Networks, communities and kronecker products

摘要

Emergence of the web and online computing applications gave rise to rich large scale social activity data. One of the principal challenges then is to build models and understanding of the structure of such large social and information networks. Here I present our work on clustering and community structure in large networks, where clusters are thought of as sets of nodes that are better connected internally than to the rest of the network. We find that large networks have very different clustering structure from well studied small social networks and graphs that are well-embeddable in a low-dimensional structure. In networks of millions of nodes tight clusters exist at only very small size scales up to around 100 nodes, while at large size scales networks becomes expander like. A network model based on Kronecker products efficiently models such core-periphery network structures. The results suggest broader implications for data analysis and machine learning in sparse and noisy high-dimensional social and information networks, where intuitive notions about cluster quality fail.