# Clustering with Simplicial Complexes

arXiv: https://arxiv.org/abs/2303.07646 · HTML: https://mlsanity.com/paper/2303.07646/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Builds on (most cited first, 6 of 6)

- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Tensor Spectral Clustering for Partitioning Higher-order Network Structures](https://mlsanity.com/paper/1502.05058/) (2015)
- [Scalable motif-aware graph clustering](https://mlsanity.com/paper/1606.06235/) (2016)

## Built on by (most cited first, 2 of 2)

- [Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal](https://mlsanity.com/paper/2311.14427/) (2023)
- [Topological Signal Processing With Unoriented Operators](https://mlsanity.com/paper/2609.25310/) (2026)

## Abstract (arXiv)

In this work, we propose a new clustering algorithm to group nodes in networks based on second-order simplices (aka filled triangles) to leverage higher-order network interactions. We define a simplicial conductance function, which on minimizing, yields an optimal partition with a higher density of filled triangles within the set while the density of filled triangles is smaller across the sets. To this end, we propose a simplicial adjacency operator that captures the relation between the nodes through second-order simplices. This allows us to extend the well-known Cheeger inequality to cluster a simplicial complex. Then, leveraging the Cheeger inequality, we propose the simplicial spectral clustering algorithm. We report results from numerical experiments on synthetic and real-world network data to demonstrate the efficacy of the proposed approach.