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higher-order connectivity patterns

Higher-order connectivity patterns are structural configurations in complex networks that describe interactions and relationships among groups of three or more interconnected nodes rather than simple pairwise connections. While conventional network analyses primarily examine individual nodes and the single edges linking them, higher-order patterns capture multi-node arrangements such as network motifs, small subgraphs, simplicial complexes, and hyperedges. These localized substructures serve as functional building blocks in complex systems, reflecting intricate organizational principles and governing dynamic processes such as information propagation, synchronization, and cluster formation across biological, social, and technological networks.

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Higher-order organization of complex networks

Higher-order organization of complex networks

Austin R. Benson, David F. Gleich, Jure Leskovec

OrganizationsPurdue UniversityStanford University

Why you should read this

Develops a scalable, mathematically rigorous framework for clustering complex networks based on higher-order subgraph patterns rather than simple edges, exposing functional modular structures in massive biological, neural, and transportation systems.

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.

Added

2026-09-25