Directed Cycle
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A Directed Cycle is a graph cycle that ...
- …
- Counter-Example(s):
- See: Vertex (Graph Theory), Simple Cycle.
References
2017
- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Cycle_(graph_theory)#Definitions Retrieved:2017-6-26.
- … A simple cycle may be defined either as a closed walk with no repetitions of vertices and edges allowed, other than the repetition of the starting and ending vertex, or as the set of edges in such a walk. The two definitions are equivalent in directed graphs, where simple cycles are also called directed cycles: the cyclic sequence of vertices and edges in a walk is completely determined by the set of edges that it uses. In undirected graphs the set of edges of a cycle can be traversed by a walk in either of two directions, giving two possible directed cycles for every undirected cycle. (For closed walks more generally, in directed or undirected graphs, the multiset of edges does not unambiguously determine the vertex ordering.) A circuit can be a closed walk allowing repetitions of vertices but not edges; however, it can also be a simple cycle, so explicit definition is recommended when it is used.