Topological exploration of chemical hypergraphs using Information theory

A chemical hypergraph represents a set of chemical reactions. Hypernodes consist of sets of substances that act as reactants or products, while hyperedges correspond to chemical reactions, linking reactants to products. Another key structure in the hypergraph is the intersection of hypernodes, representing substances that participate in multiple reactions. In this work, we study a random walker on a chemical hypergraph under two different transition probability regimes. We characterize the random walker using network entropy, highlighting differences between these regimes. Additionally, we examine the structure of hypernodes by defining chemically inspired random variables and analyzing their joint and marginal Shannon entropies, as well as their mutual information. For large N, we observe bounds in these quantities.