Higher-order organization of complex networks

TL;DR

This paper introduces a scalable framework for identifying higher-order organizational patterns in complex networks, revealing intricate structures beyond traditional node and edge analysis across various domains.

Contribution

It develops a mathematically guaranteed, scalable clustering method based on higher-order connectivity patterns, uncovering complex structures in large networks.

Findings

Higher-order organization exists in neuronal and transportation networks.

The framework scales to networks with billions of edges.

Reveals rich organizational structures beyond lower-order patterns.

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.