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I have a strongly connected component with over 200 vertices and more than 600 edges. I need to iterate through each simple cycle in the graph exhaustively, without specifying a particular node. Is there any efficient algorithm to perform this operation?

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Efficient Algorithms are already known in the literature.

See e.g.,

  • Tarjan, R E and Read, R C (1975) Bounds on backtrack algorithms for listing cycles, paths, and spanning trees. Networks 5(3):237-252

  • Johnson, D. B. (1975) Finding All the Elementary Circuits of a Directed Graph. SIAM Journal on Computing 4(1):77-84.

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