Scalable and Axiomatic Ranking of Network Role Similarity

摘要

A key task in analyzing social networks and other complex networks is role analysis: describing and categorizing nodes according to how they interact with other nodes. Two nodes have the same role if they interact with equivalent sets of neighbors. The most fundamental role equivalence is automorphic equivalence. Unfortunately, the fastest algorithms known for graph automorphism are nonpolynomial. Moreover, since exact equivalence is rare, a more meaningful task is measuring the role similarity between any two nodes. This task is closely related to the structural or link-based similarity problem that SimRank addresses. However, SimRank and other existing similarity measures are not sufficient because they do not guarantee to recognize automorphically or structurally equivalent nodes. This article makes two contributions. First, we present and justify several axiomatic properties necessary for a role similarity measure or metric. Second, we present RoleSim, a new similarity metric that satisfies these axioms and can be computed with a simple iterative algorithm. We rigorously prove that RoleSim satisfies all of these axiomatic properties. We also introduce Iceberg RoleSim, a scalable algorithm that discovers all pairs with RoleSim scores above a user-defined threshold θ. We demonstrate the interpretative power of RoleSim on both both synthetic and real datasets.