Editing Spanning tree (section)

===Fundamental cycles===
Adding just one edge to a spanning tree will create a cycle; such a cycle is called a '''fundamental cycle''' with respect to that tree. There is a distinct fundamental cycle for each edge not in the spanning tree; thus, there is a one-to-one correspondence between fundamental cycles and  edges not in the spanning tree.  For a connected graph with ''V'' vertices, any spanning tree will have ''V''&nbsp;−&nbsp;1 edges, and thus, a graph of ''E'' edges and one of its spanning trees will have ''E''&nbsp;−&nbsp;''V''&nbsp;+&nbsp;1 fundamental cycles (The number of edges subtracted by number of edges included in a spanning tree; giving the number of edges not included in the spanning tree). For any given spanning tree the set of all ''E''&nbsp;−&nbsp;''V''&nbsp;+&nbsp;1 fundamental cycles forms a [[cycle basis]], i.e., a basis for the [[cycle space]].<ref>{{harvtxt|Kocay|Kreher|2004}}, pp.&nbsp;65–67.</ref>