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.

中文翻译：

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网络角色相似度的可扩展且公理化的排名


分析社交网络和其他复杂网络的关键任务是角色分析：根据节点与其他节点的交互方式对节点进行描述和分类。如果两个节点交互，则它们具有相同的角色相等的邻居集。最基本的角色等价是自守等价。不幸的是，已知的图自同构最快的算法是非多项式的。此外，由于完全等同的情况很少见，因此更有意义的任务是衡量角色相似任意两个节点之间。此任务与 SimRank 解决的结构或基于链接的相似性问题密切相关。然而，SimRank 和其他现有的相似性度量还不够，因为它们不能保证识别自同构或结构等效的节点。本文有两个贡献。首先，我们提出并证明角色相似性度量或度量所必需的几个公理属性。其次，我们提出了 RoleSim，一种新的相似性度量，它满足这些公理，并且可以使用简单的迭代算法进行计算。我们严格证明 RoleSim 满足所有这些公理属性。我们还引入了 Iceberg RoleSim，这是一种可扩展的算法，可以发现 RoleSim 分数高于用户定义的阈值 θ 的所有配对。我们展示了 RoleSim 对合成数据集和真实数据集的解释能力。