Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Compute the branchial hypergraph of a graph
ResourceFunction["BranchialHypergraph"][g] computes the branchial hypergraph of a graph g. 
Compute branchial hyperedges of a simple graph:
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Branchial hypergraph of a mixed graph:
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The branchial hypergraph of any undirected graph is trivial:
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Make a branchial hypergraph for a simple string substitution multiway system:
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Display the branchial hypergraph using an Echo while plotting the graph:
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Usually the branchial graph can be recovered from the hypergraph by taking the first two vertices from each hyperedge:
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