Algorithms to Identify All the Cycle Bases in a UnDirected Graph?

From what I can tell, not only is Brian's hunch spot on, but an even stronger proposition holds: each edge that's not in the minimum spanning tree adds exactly one new "base cycle".

Off the top of my head, I would start by looking at any Minimum Spanning Tree algorithm (Prim, Kruskal, etc). There can't be more base cycles (If I understand it correctly) than edges that are NOT in the MST....

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