With hubris and arrogance, I implemented my own ring equivalence class finder. With humility and grace, the SSSRFinder method getRingEquivalenceClasses does better for at least one case:

This is the test case used in SimpleCycleBasisTest, and probably in the paper on the subject. I guess I should read that instead of other papers on cycle bases. I do get the same answer for cuneane as when I do it by hand. That is to say, 3 equivalence classes with [1, 2, 2] elements.

This is the test case used in SimpleCycleBasisTest, and probably in the paper on the subject. I guess I should read that instead of other papers on cycle bases. I do get the same answer for cuneane as when I do it by hand. That is to say, 3 equivalence classes with [1, 2, 2] elements.

For the 'Bauer' graph above (as I am currently calling it - Ulrich Bauer is the author of the SSSRFinder) the signature method puts almost every vertex in its own equivalence class. Now my method makes equivalence classes from cycles with the vertices in the same vertex equivalence class. Naturally enough, this makes a lot of ring equivalence classes.

The graph on the left has vertices colored by degree, to show how dissimilar the rings are. Is the SSSRFinder really getting the right answer?

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