Editing Cycle space (section)

===Existence===
By [[Veblen's theorem]],<ref>{{Citation | last1=Veblen | first1=Oswald | author1-link=Oswald Veblen | title=An application of modular equations in analysis situs | jstor=1967604 | series=Second Series | year=1912 | journal=[[Annals of Mathematics]] | volume=14 | issue=1 | pages=86–94 | doi = 10.2307/1967604 }}.</ref> every Eulerian subgraph of a given graph can be decomposed into [[Cycle (graph theory)|simple cycles]], subgraphs in which all vertices have degree zero or two and in which the degree-two vertices form a connected set. Therefore, it is always possible to find a basis in which the basis elements are themselves all simple cycles. Such a basis is called a [[cycle basis]] of the given graph. More strongly, it is always possible to find a basis in which the basis elements are [[Induced path|induced cycles]] or even (in a [[k-vertex-connected graph|3-vertex-connected graph]]) [[vertex separator|non-separating]] induced cycles.<ref>{{harvtxt|Diestel|2012}}, pp.&nbsp;32,&nbsp;65.</ref>