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The term cycle may also refer to an element of the cycle space of a graph. There are many cycle spaces, one for each coefficient field or ring. The most common is the binary cycle space (usually called simply the cycle space), which consists of the edge sets that have even degree at every vertex; it forms a vector space over the two-element field.
The circuit rank of a hypergraph can be derived by its Levi graph, with the same circuit rank but reduced to a simple graph. r = g + c − ( v + e ) {\displaystyle r=g+c-(v+e)} where g is the degree sum , e is the number of edges in the given graph, v is the number of vertices , and c is the number of connected components .
A directed cycle graph of length 8. A directed cycle graph is a directed version of a cycle graph, with all the edges being oriented in the same direction. In a directed graph, a set of edges which contains at least one edge (or arc) from each directed cycle is called a feedback arc set.
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