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Inferring coarse views of connectivity in very large graphs

This paper presents a simple framework, called WalkAbout, to infer a coarse view of connectivity in very large graphs; that is, identify well-connected "regions" with different edge densities and determine the corresponding inter- and intra-region connectivity. We leverage the transient behavior of many short random walks (RW) on a large graph that is assumed to have regions of varying edge density but whose structure is otherwise unknown. The key idea is that as RWs approach the mixing time of a region, the ratio of the number of visits by all RWs to the degree for nodes in that region converges to a value proportional to the average node degree in that region. Leveraging this indirect sign of connectivity enables our proposed framework to effectively scale with graph size.
 After describing the design of WalkAbout, we demonstrate the capabilities of WalkAbout by applying it to three major OSNs ie Flickr, Twitter, and Google+) and obtaining a coarse view of their connectivity structure. In addition, we illustrate how the communities that are obtained by running a popular community detection method on these OSNs stack up against the WalkAbout-discovered regions. Finally, we examine the "meaning" of the regions obtained by WalkAbout, and demonstrate that users in the identified regions exhibit common social attributes.