Vertex neighborhoods, low conductance cuts, and good seeds for local community methods

The communities of a social network are sets of vertices with more connections inside the set than outside. We theoretically demonstrate that two commonly observed properties of social networks, heavy-tailed degree distributions and large clustering coefficients, imply the existence of vertex neighborhoods (also known as egonets) that are themselves good communities. We evaluate these neighborhood communities on a range of graphs. What we find is that the neighborhood communities can exhibit conductance scores that are as good as the Fiedler cut. Also, the conductance of neighborhood communities shows similar behavior as the network community profile computed with a personalized PageRank community detection method. Neighborhood communities give us a simple and powerful heuristic for speeding up local partitioning methods. Since finding good seeds for the PageRank clustering method is difficult, most approaches involve an expensive sweep over a great many starting vertices. We show ...

• Type: Journal
• Year: 2012
• Where: KDD
• Authors: David F. Gleich, C. Seshadhri
• Keywords: Data Mining, KDD 2012, Lockheed Martin Corporation, Nuclear Security Administration, Sandia National Laboratories