  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.
