k-simplex2vec: a simplicial extension of node2vec

TL;DR

This paper introduces k-simplex2vec, an extension of node2vec that embeds higher-dimensional simplices into Euclidean space, enabling advanced analysis of complex higher-order network interactions.

Contribution

It proposes a novel method to embed simplicial complexes into Euclidean space, extending node2vec to higher dimensions for better structural insights.

Findings

Provides a new way to analyze higher-order interactions in graphs

Enables use of simplicial complexes as input for machine learning models

Offers insights into the structure of complex networks

Abstract

We present a novel method of associating Euclidean features to simplicial complexes, providing a way to use them as input to statistical and machine learning tools. This method extends the node2vec algorithm to simplices of higher dimensions, providing insight into the structure of a simplicial complex, or into the higher-order interactions in a graph.