Every strongly 2-connected digraph can be generated from the digraph A4 and bidirected cycles by basic, chain, collarette, and bracelet augmentations, and any two such digraphs linked by a butterfly-minor are connected by a sequence of these operations.
Brace generation
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Generating strongly 2-connected digraphs
Every strongly 2-connected digraph can be generated from the digraph A4 and bidirected cycles by basic, chain, collarette, and bracelet augmentations, and any two such digraphs linked by a butterfly-minor are connected by a sequence of these operations.