Hypergraph-Based Models of Random Chemical Reaction Networks: Conservation Laws, Connectivity, and Percolation

Random graph models have been instrumental in characterizing complex networks, but chemical reaction networks (CRNs) are better represented as hypergraphs. Traditional models of random CRNs often reduce CRNs to bipartite graphs, representing species and reactions as distinct nodes, or simpler derived graphs, which can obscure the relationship between the statistical properties of these representations and the physical characteristics of the CRN. We introduce a straightforward model for generating random CRNs that preserves their hypergraph structure as well as atomic composition, enabling the direct study of chemically relevant features. Notably, our approach distinguishes two notions of connectivity that are equivalent in graphs but differ fundamentally in hypergraphs. These notions exhibit percolation-like phase transitions, which we analyze in detail. The first type of connectivity has relevance to steady-state synthesis and transduction, determining the effective reactions an open CRN can perform at steady state. The second type is suitable to identify which species can be produced from a given initial set of species in a closed CRN. Our findings highlight the importance of hypergraph-based modeling for uncovering the complex behaviors of CRNs.