Molecular Line HyperGraphs and SuperHyperGraphs

Abstract. Hypergraphs extend classical graphs by allowing hyperedges to connect any nonempty subset ofvertices, thereby capturing complex group-level relationships. Superhypergraphs advance this framework byintroducing recursively nested powerset layers, which represent hierarchical and self-referential connectionsamong hyperedges. A line graph encodes edge adjacencies of a given graph by turning each edge into a vertexand joining two such vertices when the corresponding edges share an endpoint. An iterated line graph appliesthis construction repeatedly, each time to the result of the previous step. Within chemistry, molecular andchemical graphs are well established, and hypergraphs, line graphs, and superhypergraphs have also beenexplored in this setting. In this paper, we introduce Molecular Line SuperHyperGraphs and Molecular IteratedLine SuperHyperGraphs, provide formal definitions, and discuss potential applications. We expect that theseframeworks will enable clearer and more faithful representations of hierarchical molecular structure in chemistry. Keywords: SuperHyperGraph, HyperGraph, Line Graph, Molecular Graph, Iterated Line Graph