The tendency for real-world networks to cluster is the basis for many models and algorithms used to study complex systems, and the standard measurement of this tendency is the clustering coefficient, which is the probability that a length-2 path is “closed”, i.e., induces a triangle. 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, which measure the closure probability of higher-order cliques. These higher-order clustering coefficients reveal new insights into how real-world networks cluster.
Postdoc, Computer Science