Assembly in Directed Hypergraphs

doi:10.1098/rspa.2025.0331

Assembly in Directed Hypergraphs

2025-10-15

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DOI：10.1098/rspa.2025.0331

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Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to generalize the notion of assembly to general chemical reaction systems and to make explicit the connection to rule-based models of chemistry, in particular DPO graph rewriting. We observe, furthermore, that assembly theory is closely related to retrosynthetic analysis in chemistry. The assembly index fits seamlessly into a large family of cost measures for directed hyperpath problems that also encompasses cost functions used in computational synthesis planning. This allows us to devise a generic approach to compute complexity measures derived from minimal hyperpaths in rule-derived directed hypergraphs using integer linear programming.

Keywords:

assembly index

retrosynthesis

directed hypergraphs

B-hypergraphs

hyperpath problems

graph rewriting

Assembly in Directed Hypergraphs

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