Talk:Cycle space

The elements of the cycle space can be characterized by the cuts: A set of edges is an element of the cycle space if and only if it meets every cut in a finite number of edges.

This can't be quite right, since in a finite graph any set of edges would qualify. AxelBoldt 21:11, 24 Feb 2004 (UTC)

fundamental cycles?[edit]

Article currently states:

It is not necessary to use all cycles to generate the cycle space: if G is connected and any spanning tree T of G is given, then the fundamental cycles of T form a basis of the cycle space.

I don't really understand what this is saying. Clearly, adding just one edge to a spanning tree makes a cycle, and also its clear that one gets one unique cycle for every edge that is not in the spanning tree. Is this the definition of a "fundamental cycle"? linas (talk) 23:12, 7 September 2008 (UTC)[reply]

Never mind, yes, this is the definition. linas (talk) 01:39, 8 September 2008 (UTC)[reply]

Homology[edit]

Shouldnt the article mention that if the graph is considered as a topological space the cycle space is natually identified with the first homology group?81.101.138.148 (talk) 10:02, 14 October 2011 (UTC) That was me Billlion (talk) 10:03, 14 October 2011 (UTC)[reply]

Yes, that would be a good idea. —David Eppstein (talk) 14:38, 14 October 2011 (UTC)[reply]