title: Higher-order organization of complex networks.
abstract: Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks--at the level of small network subgraphs--remains largely unknown. Here, we develop a generalized framework for clustering networks on the basis of higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks, including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns.
authors.affiliation: Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA.
authors.forename: Austin R
authors.initials: AR
authors.lastname: Benson
authors.affiliation: Department of Computer Science, Purdue University, West Lafayette, IN 47906, USA.
authors.forename: David F
authors.initials: DF
authors.lastname: Gleich
authors.affiliation: Computer Science Department, Stanford University, Stanford, CA 94305, USA. jure@cs.stanford.edu.
authors.forename: Jure
authors.initials: J
authors.lastname: Leskovec