We describe the vertex collocation profile (VCP) concept. VCPs provide rich information about the surrounding local structure of embedded vertex pairs. VCP analysis offers a new tool for researchers and 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 the VCP method its analytical power also enables it to perform well when used to accomplish link prediction. We first develop the theory, mathematics, and algorithms underlying VCPs. We provide timing results to demonstrate that the algorithms scale well even for large networks. Then we demonstrate VCP methods performing link prediction competitively with unsupervised and supervised methods across different network families. Unlike many analytical tools, VCPs inherently generalize to multirelational data, which provides them with unique power in complex modeling tasks. To demonstrate this, we apply the VCP method to longitudinal networks by encoding temporally resolved information into different relations. In this way, the transitions between VCP elements represent temporal evolutionary patterns in the longitudinal network data. Results show that VCPs can use this additional data, typically challenging to employ, to improve predictive model accuracies. We conclude with our perspectives on the VCP method and its future in network science, particularly link prediction.
Keywords: Graph theory; Isomorphism; Link prediction; Network analysis.