Cycle Enumeration Of An Undirected Graph With Multi Edges

I'm trying to code a program that uses Electrical Mesh Analasys. So I have the nodes of the circuit [A,B,C,D] and the branches that links the nodes [0,1,2,3,4,5,6,7,8]. How can I f

Solution 1:

You can make a spanning tree using any algorithm you like (BFS works).

Then, for every edge that's not in the tree, you make a cycle containing that edge plus the path through the tree from one end to the other.