Vertex collocation profiles

We introduce the concept of a vertex collocation profile (VCP) for the purpose of topological link analysis and prediction. VCPs provide nearly complete information about the surrounding local structure of embedded vertex pairs. The VCP approach offers a new tool for domain experts to understand the underlying growth mechanisms in their networks and to analyze link formation mechanisms in the appropriate sociological, biological, physical, or other context. The same resolution that gives VCP its analytical power also enables it to perform well when used in supervised models to discriminate potential new links. We first develop the theory, mathematics, and algorithms underlying VCPs. Then we demonstrate VCP methods performing link prediction competitively with unsupervised and supervised methods across several different network families. We conclude with timing results that introduce the comparative performance of several existing algorithms and the practicability of VCP computations on large networks.