Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs
<|reference_start|>Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs: 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.<|reference_end|>
@article{battistella2024understanding,
    title={Understanding High-Order Network Structure using Permissible Walks on
  Attributed Hypergraphs},
    author={Enzo Battistella, Sean English, Robert Green, Cliff Joslyn, Evgeniya
  Lagoda, Van Magnan, Audun Myers, Evan D. Nash, Michael Robinson},
    journal={arXiv preprint arXiv:2405.04559},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.04559},
    primaryClass={cs.SI math.CO}
}