Large chemical networks appear in various branches of chemistry and biology, in particular, cellular metabolism and prebiotic chemistry. Detailed simulations of such networks are difficult, or even impossible for lack of kinetic data. Various strategies have been developed to produce synthetic random networks mimicking the large scale organizational properties of experimental chemical networks. These random networks are however mathematical artifacts, which fail to reflect the general reactivity structure of chemistry. We present here a class of random models of prebiotic (uncatalyzed) chemistry, based on context-independent rules, which is coherent with the general compositional logic of metabolism. The general organization of the random networks fits within the small-world paradigm. We get a phase diagram of the models through an approximate mapping to a solvable tree growth model. Our predictions go beyond a purely abstract connectivity analysis of the reaction graph by studying the diversity of chemical mechanisms, and singling out evolutionary patterns, such as autocatalysis and multistationarity, paving the road to possible open-ended evolution.

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• Network evolution
• Chemical networks
• Random graphs
• Small-world model