Counting chemical reaction networks with NAUTY

TL;DR

This paper presents a methodology for enumerating all nonisomorphic chemical reaction networks within various classes, facilitating the study of their properties and behaviors by providing comprehensive, non-redundant lists.

Contribution

It introduces a systematic approach to list all nonisomorphic CRNs in different classes using NAUTY, aiding researchers in analyzing network diversity and properties.

Findings

Generated comprehensive lists of nonisomorphic CRNs

Applied methodology to various classes of CRNs

Provided an online database of the networks

Abstract

It is useful to have complete lists of nonisomorphic chemical reaction networks (CRNs) of a given size, with or without various restrictions. One may, for example, be interested in exploring how often certain dynamical behaviours occur in small CRNs, or wish to find examples to illustrate some aspect of the theory. In such cases, it is natural to examine one representative from each isomorphism class of CRNs. Inspired by the related project of Deckard et al (Enumeration and online library of mass-action reaction networks. http://arXiv.org/abs/0901.3067, 2009), this document outlines the methodology involved in listing all CRNs in various classes of interest including, for example, general CRNs, dynamically nontrivial CRNs, weakly reversible CRNs, fully open CRNs, etc. The accompanying data (i.e., lists of nonisomorphic CRNs in the various classes) is at https://reaction-networks.net/networks/. Note that both document and data are work in progress.