# Higher-order clustering in networks

arXiv: https://arxiv.org/abs/1704.03913 · HTML: https://mlsanity.com/paper/1704.03913/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2017.

## Built on by (most cited first, 7 of 7)

- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Hypergraph Artificial Benchmark for Community Detection (h-ABCD)](https://mlsanity.com/paper/2210.15009/) (2022)
- [Sparse random hypergraphs: Non-backtracking spectra and community detection](https://mlsanity.com/paper/2203.07346/) (2022)
- [Modularity Based Community Detection in Hypergraphs](https://mlsanity.com/paper/2406.17556/) (2024)
- [A Graph Data Augmentation Strategy with Entropy Preservation](https://mlsanity.com/paper/2107.06048/) (2021)
- [A Network Science perspective of Graph Convolutional Networks: A survey](https://mlsanity.com/paper/2301.04824/) (2023)
- [Modeling Hypergraph Using Large Language Models](https://mlsanity.com/paper/2510.11728/) (2025)

## Abstract (arXiv)

A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a triangle in the network. However, higher-order cliques beyond triangles are crucial to understanding complex networks, and the clustering behavior with respect to such higher-order network structures is not well understood. Here we introduce higher-order clustering coefficients that measure the closure probability of higher-order network cliques and provide a more comprehensive view of how the edges of complex networks cluster. Our higher-order clustering coefficients are a natural generalization of the traditional clustering coefficient. We derive several properties about higher-order clustering coefficients and analyze them under common random graph models. Finally, we use higher-order clustering coefficients to gain new insights into the structure of real-world networks from several domains.