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Higher-order clustering in networks

Abstract · Apr 12, 2017 19:48 ·

clustering coefficient triangle closure edges coefficients wedges order triangles higher cs-si cond-mat-stat-mech physics-soc-ph stat-ml

Arxiv Abstract

  • Hao Yin
  • Austin R. Benson
  • Jure Leskovec

A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order structures beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order patterns is not well understood. Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network structures and provide a more comprehensive view of how the edges of complex networks cluster. Our higher-order clustering coefficients are a natural generalization of the traditional clustering coefficient. We derive several properties about higher-order clustering coefficients and analyze them under common random graph models. Finally, we use higher-order clustering coefficients to gain new insights into the structure of real-world networks from several domains.

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