Independent cycles in undirected graph

Question

What is the algorithm that allows me to determine the independent cycles in an undirected graph. For example, in the figure below: The independent cycles: [2-12-4-5-13-2] [4-5-6-4] [4-10-11-7-6-4] Thanxs

Answer 1

Start with a spanning tree and consider the graphs you get by adding a single edge of your graph.

Answer 2

@Robert Israel

Suppose we have the graph below .Using your method, I will get 2 cycles : [8-2-3-8] and [8-2-4-5-3-8].

But I want to get [8-2-3-8] and [2-4-5-3-2].

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