  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.
