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Asked: 2026-06-02T06:19:48+00:00

Respected Sir, I am working with a specific graphical structure representing 2-player normal form

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Respected Sir,

I am working with a specific graphical structure representing 2-player normal form games (game theory). I know that I can compute all strongly connected components of the directed graph in O(V+E) via Tarjans, but was wondering what the complexity of computing all of the simple cycles of a strongly connected component is? AND, if there is a known upper bound on the number of such simple cycles given the number of vertices defining the strongly connected component?

I am looking for any literature/algorithms related to both of these problems. THANK YOU!

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  1. Editorial Team

    In your case the number of possible simple 2k-cycles are (n choose k) * (m choose k). If n, m, and k are not small, this grows exponentially.

    Enumerating the cycles is not feasible. I doubt that it is possible to count them for an arbitrary graph in reasonable time. Even with dynamic programming techniques this takes exponential time and space (but with a lower exponent than without those techniques).

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