Axiomatic ranking of network role similarity

A key task in analyzing social networks and other complex networks is role analysis: describing and categorizing nodes by 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 algorithm known for graph automorphism is 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 link-based similarity problem that SimRank addresses. However, SimRank and other existing simliarity measures are not sufficient because they do not guarantee to recognize automorphically or structurally equivalent nodes. This paper makes two contributions. First, we present and justify several axiomatic properties necessary for a role similarity measure or metric. Second, we present RoleSim, a role similarity metric which satisfies these axioms and which can be computed with a simple iterative algorithm. We rigorously prove that RoleSim satisfies all the axiomatic properties and demonstrate its superior interpretative power on both synthetic and real datasets.

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