'''Cycle''' in Graph_theory and Computer_science has several meanings:
* A closed walk, with repeated vertices allowed. See Path_(graph_theory). (This usage is common in computer science. In graph theory it is more often called a '''closed walk'''.)
* A closed (simple) path, with no other repeated vertices than the starting and ending vertices. (This usage is common in graph theory.) This may also be called a '''simple cycle''', '''circuit''', '''circle''', or '''polygon'''.
* A closed directed walk, with repeated vertices allowed. (This usage is common in computer science. In graph theory it is more often called a '''closed directed walk'''.)
* A closed directed (simple) path, with no repeated vertices other than the starting and ending vertices. (This usage is common in graph theory.) This may also be called a '''simple (directed) cycle'''.
* The edge set of an undirected closed path without repeated vertices. This may also be called a '''circuit''', '''circle''', or '''polygon'''.
* An element of the binary or integral (or real, complex, etc.) Cycle_space of a graph. (This is the usage closest to that in the rest of mathematics, in particular Algebraic_topology.) Such a cycle may be called a '''binary cycle''', '''integral cycle''', etc.
* An edge set which has even degree at every vertex; also called an '''even edge set''' or, when taken together with its vertices, an '''even subgraph'''. This is equivalent to a binary cycle, since a binary cycle is the Indicator_function of an edge set of this type.
== See also ==
* Cycle_graph
* Path_(graph_theory)
Category:Graph_theory Category:Mathematical_disambiguation
Fr:Cycle_(graphe)
Ja:閉路
Pl:Cykl_(teoria_grafów)