# Simplex2Vec embeddings for community detection in simplicial complexes

arXiv: https://arxiv.org/abs/1906.09068 · HTML: https://mlsanity.com/paper/1906.09068/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 13 of 13)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Simplicial Complex Representation Learning](https://mlsanity.com/paper/2103.04046/) (2021)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [CAT-Walk: Inductive Hypergraph Learning via Set Walks](https://mlsanity.com/paper/2306.11147/) (2023)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Learning distributed representations with efficient SoftMax normalization](https://mlsanity.com/paper/2303.17475/) (2023)
- [Information Filtering Networks: Theoretical Foundations, Generative Methodologies, and Real-World Applications](https://mlsanity.com/paper/2505.03812/) (2025)
- [Learning From Simplicial Data Based on Random Walks and 1D Convolutions](https://mlsanity.com/paper/2404.03434/) (2024)
- [Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networks](https://mlsanity.com/paper/2507.16347/) (2025)
- [Modern Structure-Aware Simplicial Spatiotemporal Neural Network](https://mlsanity.com/paper/2604.15833/) (2026)
- [TopoEmbedX: A General Framework for Representation Learning on Topological Domains](https://mlsanity.com/paper/2609.37884/) (2026)

## Abstract (arXiv)

Topological representations are rapidly becoming a popular way to capture and encode higher-order interactions in complex systems. They have found applications in disciplines as different as cancer genomics, brain function, and computational social science, in representing both descriptive features of data and inference models. While intense research has focused on the connectivity and homological features of topological representations, surprisingly scarce attention has been given to the investigation of the community structures of simplicial complexes. To this end, we adopt recent advances in symbolic embeddings to compute and visualize the community structures of simplicial complexes. We first investigate the stability properties of embedding obtained for synthetic simplicial complexes to the presence of higher order interactions. We then focus on complexes arising from social and brain functional data and show how higher order interactions can be leveraged to improve clustering detection and assess the effect of higher order interaction on individual nodes. We conclude delineating limitations and directions for extension of this work.