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FindFundamentalCycles

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Fundamental cycle basis from a BFS spanning forest in reverse edge order

FindFundamentalCycles[g]
g = WheelGraph[4]; basis = FindFundamentalCycles[g] → {{4  1, 1  3, 3  4}, {4  1, 1  2, 2  4}, {3  1, 1  2, 2  3}}

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