Speaker
Description
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
preserve their hypergraph structure and 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.
