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- Cycle_(graph_theory) abstract "In graph theory, there are several different types of object called cycles, principally a closed walk and a simple cycle; also, e.g., an element of the cycle space of the graph. A closed walk consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph. In a directed graph, each edge must be traversed by the walk consistently with its direction: the edge must be oriented from the earlier of two consecutive vertices to the later of the two vertices in the sequence. The choice of starting vertex is not important: traversing the same cyclic sequence of edges from different starting vertices produces the same closed walk.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.In this article \"cycle\" means a simple cycle, except where otherwise stated.".
- Cycle_(graph_theory) thumbnail Graph_cycle.gif?width=300.
- Cycle_(graph_theory) wikiPageID "168609".
- Cycle_(graph_theory) wikiPageLength "11076".
- Cycle_(graph_theory) wikiPageOutDegree "53".
- Cycle_(graph_theory) wikiPageRevisionID "701921361".
- Cycle_(graph_theory) wikiPageWikiLink Algebraic_topology.
- Cycle_(graph_theory) wikiPageWikiLink Basis_(linear_algebra).
- Cycle_(graph_theory) wikiPageWikiLink Bipartite_graph.
- Cycle_(graph_theory) wikiPageWikiLink Bridge_(graph_theory).
- Cycle_(graph_theory) wikiPageWikiLink Cactus_graph.
- Cycle_(graph_theory) wikiPageWikiLink Cage_(graph_theory).
- Cycle_(graph_theory) wikiPageWikiLink Category:Graph_theory_objects.
- Cycle_(graph_theory) wikiPageWikiLink Chordal_graph.
- Cycle_(graph_theory) wikiPageWikiLink Complement_graph.
- Cycle_(graph_theory) wikiPageWikiLink Computer_cluster.
- Cycle_(graph_theory) wikiPageWikiLink Cycle_basis.
- Cycle_(graph_theory) wikiPageWikiLink Cycle_double_cover.
- Cycle_(graph_theory) wikiPageWikiLink Cycle_graph.
- Cycle_(graph_theory) wikiPageWikiLink Cycle_space.
- Cycle_(graph_theory) wikiPageWikiLink Deadlock.
- Cycle_(graph_theory) wikiPageWikiLink Depth-first_search.
- Cycle_(graph_theory) wikiPageWikiLink Directed_acyclic_graph.
- Cycle_(graph_theory) wikiPageWikiLink Eulerian_path.
- Cycle_(graph_theory) wikiPageWikiLink Finite_field.
- Cycle_(graph_theory) wikiPageWikiLink Girth_(graph_theory).
- Cycle_(graph_theory) wikiPageWikiLink Graph_theory.
- Cycle_(graph_theory) wikiPageWikiLink Hamiltonian_path.
- Cycle_(graph_theory) wikiPageWikiLink Induced_path.
- Cycle_(graph_theory) wikiPageWikiLink Leonhard_Euler.
- Cycle_(graph_theory) wikiPageWikiLink Module_(mathematics).
- Cycle_(graph_theory) wikiPageWikiLink Multiset.
- Cycle_(graph_theory) wikiPageWikiLink NP-completeness.
- Cycle_(graph_theory) wikiPageWikiLink Ores_theorem.
- Cycle_(graph_theory) wikiPageWikiLink Perfect_graph.
- Cycle_(graph_theory) wikiPageWikiLink Peripheral_cycle.
- Cycle_(graph_theory) wikiPageWikiLink Pseudoforest.
- Cycle_(graph_theory) wikiPageWikiLink Ring_(mathematics).
- Cycle_(graph_theory) wikiPageWikiLink Rocha–Thatte_cycle_detection_algorithm.
- Cycle_(graph_theory) wikiPageWikiLink Route_inspection_problem.
- Cycle_(graph_theory) wikiPageWikiLink Seven_Bridges_of_Königsberg.
- Cycle_(graph_theory) wikiPageWikiLink Strong_perfect_graph_theorem.
- Cycle_(graph_theory) wikiPageWikiLink Strongly_connected_component.
- Cycle_(graph_theory) wikiPageWikiLink Time_complexity.
- Cycle_(graph_theory) wikiPageWikiLink Topological_sorting.
- Cycle_(graph_theory) wikiPageWikiLink Triangle-free_graph.
- Cycle_(graph_theory) wikiPageWikiLink Veblens_theorem.
- Cycle_(graph_theory) wikiPageWikiLink Vector_space.
- Cycle_(graph_theory) wikiPageWikiLink Vertex_(graph_theory).
- Cycle_(graph_theory) wikiPageWikiLink Wait-for_graph.
- Cycle_(graph_theory) wikiPageWikiLink File:Graph_cycle.gif.
- Cycle_(graph_theory) wikiPageWikiLinkText "Cycle (graph theory)".
- Cycle_(graph_theory) wikiPageWikiLinkText "Cycle (graph theory)#Cycle detection".
- Cycle_(graph_theory) wikiPageWikiLinkText "Cycles".
- Cycle_(graph_theory) wikiPageWikiLinkText "acyclic".
- Cycle_(graph_theory) wikiPageWikiLinkText "circuit".
- Cycle_(graph_theory) wikiPageWikiLinkText "circuits".
- Cycle_(graph_theory) wikiPageWikiLinkText "circular relationships".
- Cycle_(graph_theory) wikiPageWikiLinkText "closed circuit".
- Cycle_(graph_theory) wikiPageWikiLinkText "cycle (graph theory)".
- Cycle_(graph_theory) wikiPageWikiLinkText "cycle".
- Cycle_(graph_theory) wikiPageWikiLinkText "cycle-free".
- Cycle_(graph_theory) wikiPageWikiLinkText "cycles".
- Cycle_(graph_theory) wikiPageWikiLinkText "cyclic relations".
- Cycle_(graph_theory) wikiPageWikiLinkText "cyclic".
- Cycle_(graph_theory) wikiPageWikiLinkText "directed cycle".
- Cycle_(graph_theory) wikiPageWikiLinkText "simple cycle".
- Cycle_(graph_theory) wikiPageWikiLinkText "simple cycles".
- Cycle_(graph_theory) wikiPageUsesTemplate Template:Reflist.
- Cycle_(graph_theory) subject Category:Graph_theory_objects.
- Cycle_(graph_theory) hypernym Types.
- Cycle_(graph_theory) type MeanOfTransportation.
- Cycle_(graph_theory) type Object.
- Cycle_(graph_theory) comment "In graph theory, there are several different types of object called cycles, principally a closed walk and a simple cycle; also, e.g., an element of the cycle space of the graph. A closed walk consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph.".
- Cycle_(graph_theory) label "Cycle (graph theory)".
- Cycle_(graph_theory) sameAs Q245595.
- Cycle_(graph_theory) sameAs Kreds_(graf).
- Cycle_(graph_theory) sameAs Zyklus_(Graphentheorie).
- Cycle_(graph_theory) sameAs Cycle_(théorie_des_graphes).
- Cycle_(graph_theory) sameAs Kör_(gráfelmélet).
- Cycle_(graph_theory) sameAs 閉路.
- Cycle_(graph_theory) sameAs 순환_(그래프_이론).
- Cycle_(graph_theory) sameAs Cykl_(teoria_grafów).
- Cycle_(graph_theory) sameAs Ciclo_(teoria_de_grafos).
- Cycle_(graph_theory) sameAs Цикл_(теория_графов).
- Cycle_(graph_theory) sameAs Цикл_(теорія_графів).
- Cycle_(graph_theory) sameAs Chu_trình_(lý_thuyết_đồ_thị).
- Cycle_(graph_theory) sameAs Q245595.
- Cycle_(graph_theory) sameAs 環_(圖論).
- Cycle_(graph_theory) wasDerivedFrom Cycle_(graph_theory)?oldid=701921361.
- Cycle_(graph_theory) depiction Graph_cycle.gif.
- Cycle_(graph_theory) isPrimaryTopicOf Cycle_(graph_theory).