Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs

TL;DR

This paper introduces a new framework for analyzing high-order network structures in hypergraphs through permissible walks, leveraging hypergraph attributions to better understand complex, attributed networks.

Contribution

It presents a novel generalization of walks in hypergraphs using permissible walk graphs that incorporate hypergraph attributions, unifying previous methods.

Findings

Applied to Reddit data with temporal hyperedges

Demonstrated the framework's ability to incorporate categorical and temporal attributions

Showed improved understanding of high-order network dynamics

Abstract

Hypergraphs have been a recent focus of study in mathematical data science as a tool to understand complex networks with high-order connections. One question of particular relevance is how to leverage information carried in hypergraph attributions when doing walk-based techniques. In this work, we focus on a new generalization of a walk in a network that recovers previous approaches and allows for a description of permissible walks in hypergraphs. Permissible walk graphs are constructed by intersecting the attributed $s$-line graph of a hypergraph with a relation respecting graph. The attribution of the hypergraph's line graph commonly carries over information from categorical and temporal attributions of the original hypergraph. To demonstrate this approach on a temporally attributed example, we apply our framework to a Reddit data set composed of hyperedges as threads and authors as nodes where post times are tracked.