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cycle (graph theory)

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Cycle (graph theory)
In graph theory, there are two different types of object called cycles; a closed walk and a simple cycle. 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. A simple cycle, also called a circle or polygon, is a closed walk with no repetitions of vertices and edges allowed, other than the repetition of the starting and ending vertex. Simple cycles may also be described by their sets of edges, unlike closed walks for which 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, the term is also sometimes used to describe a simple cycle, so explicit definition is recommended when it is used. A directed cycle in a directed graph is a sequence of vertices starting and ending at the same vertex such that, for each two consecutive vertices of the cycle, there exists an edge directed from the earlier vertex to the later one; the same distinction between closed walks and simple cycles may be made in the directed case.

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Zyklus (Graphentheorie)
Ein Zyklus oder Kreis ist in der Graphentheorie ein Weg in einem Graphen, bei dem Start- und Endknoten gleich sind. Ein zyklischer Graph ist ein Graph mit mindestens einem Zyklus. Algorithmen zum Auffinden von Zyklen in einem Graphen sind eine modifizierte topologische Sortierung oder eine modifizierte Tiefensuche.

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Cycle (théorie des graphes)
Dans un graphe non orienté, un cycle est une suite d'arêtes consécutives (chaine) dont les deux sommets extrémités sont identiques. Dans les graphes orientés, la notion équivalente est celle de circuit, même si on parle parfois aussi de cycle (par exemple dans l'expression graphe acyclique orienté).

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Cykl (teoria grafów)
Rodzaje cykli
Cykl prosty to droga zamknięta, czyli taka, której koniec (ostatni wierzchołek) jest identyczny z początkiem (pierwszym wierzchołkiem).

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閉路(へいろ、, circuit, closed walk)あるいは閉道(へいどう、)とは、始点と終点が同じのこと。すなわち、出発点に戻るような辿り方のことである。グラフ理論位相幾何学において用いられる。


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