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

Enzo Battistella; Sean English; Robert Green; Cliff Joslyn; Evgeniya Lagoda; Van Magnan; Audun Myers; Evan D. Nash; Michael Robinson

arXiv · 2405.04559

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

Enzo Battistella·Sean English·Robert Green·Cliff Joslyn·Evgeniya Lagoda·Van Magnan·Audun Myers·Evan D. Nash·Michael Robinson

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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.

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Enzo Battistella, Sean English, Robert Green, Cliff Joslyn, Evgeniya Lagoda, Van Magnan, Audun Myers, Evan D. Nash, Michael Robinson. 2024-05-07. Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs. https://arxiv.org/abs/2405.04559

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