cycle (812B)
1 # Cycle 2 3 A [simple_path] from one [vertex] to itself (= the path is simple except that the first vertex is equal to the last) 4 5 In [undirected_graphs], cycles are typically required to have length at least 3 ([triangle]). 6 7 In [directed_graphs], two vertices u and v with an [edge] from u to v and another [edge] from v to u can count as a cycle; 8 - [self_loops] can arguably count as a cycle as well 9 10 Variants: 11 - [circuit_graph] if the same [vertices] (but not [edges]) can be visited multiple times 12 - like a [trail] compared to a [simple_path] 13 - [tour] if the same [vertices] and [edges] can be visited multiple times 14 - like a [walk] compared to a [simple_path] 15 16 - [cycle_induced] 17 18 Special cases: 19 20 - [hamiltonian_cycle] 21 - [eulerian_cycle] 22 23 Up: [graph_basic_notions] 24 25 Aliases: cycles 26 27 See also: [2_regular]