Higher-order organization of complex networks

TLDR

Networks are a fundamental tool for understanding complex systems, yet higher-order organization at the subgraph level remains largely unknown. The study develops a generalized framework for clustering networks based on higher-order connectivity patterns. The framework clusters networks by exploiting higher-order connectivity patterns. The framework provides optimality guarantees, scales to billions of edges, and uncovers rich higher-order structures in neuronal and transportation 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 based on 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.