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[[Image:6n-graph2.svg|thumb|AUn graphgrafo withcon aun loopbucle onen vertexel vértice 1.]]
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En [[teoría de grafos]], un '''bucle''' o '''loop''' es una [[arista (teoría de grafos)|arista]] que conecta un [[vértice (teoría de grafos)|vértice]] consigo mismo. Un [[grafo simple]] no posee bucles.
[[Image:6n-graph2.svg|thumb|A graph with a loop on vertex 1]]
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In [[graph theory]], a '''loop''' (also called a '''self-loop''') is an [[edge (graph theory)|edge]] that connects a [[vertex (graph theory)|vertex]] to itself. A [[Graph (mathematics)#Simple_Graph|simple graph]] contains no loops.
 
Dependiendo del contexto, un [[grafo]] o [[multigrafo]] puede estar definido o no para permitir en él la presencia de bucles
Depending on the context, a [[graph (mathematics)|graph]] or a [[multigraph]] may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing [[multiple edges]] between the same vertices):
 
== NotesGrados ==
*Where graphs are defined so as to ''allow'' loops and multiple edges, a graph without loops is often called a [[multigraph]].<ref> For example, see Balakrishnan, p. 1, and Gross (2003), p. 4, Zwillinger, p. 220.</ref>
*Where graphs are defined so as to ''disallow'' loops and multiple edges, a multigraph or a [[pseudograph]] is often defined to mean a "graph" which ''can'' have loops and multiple edges.<ref>For example, see. Bollobas, p. 7, Diestel, p. 25, and Harary, p. 10.</ref>
 
Para un [[grafo no dirigido]], el [[grado (teoría de grafos)|grado]] de un vértice es igual al número de [[nodos vecinos|vértices adyacentes]]. Sin embargo, si un vértice posee un bucle, debemos añadir ''dos'' a su grado. Esto es porque cada conexión de la arista del bucle cuenta como su propio vértice adyacente; o en otras palabras, un vértice con un bucle ''se ve'' a sí mismo como un nodo adyacente a ''ambos'' vértices finales de la arista.
==Degree==
For an [[undirected graph]], the [[degree (graph theory)|degree]] of a vertex is equal to the number of [[adjacent vertex|adjacent vertices]].
 
Para un [[grafo dirigido]], un bucle añade ''uno'' al [[grado (teoría de grafos)|grado de entrada]] y ''uno'' al [[grado (teoría de grafos)|grado de salida]].
A special case is a loop, which adds two to the degree. This can be understood by letting each connection of the loop edge count as its own adjacent vertex. In other words, a vertex with a loop "sees" itself as an adjacent vertex from ''both'' ends of the edge thus adding two, not one, to the degree.
 
== Referencias ==
For a [[directed graph]], a loop adds one to the [[in degree (graph theory)|in degree]] and one to the [[out degree (graph theory)|out degree]]
 
== Notes==
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==References==
* Balakrishnan, V. K.; ''Graph Theory'', McGraw-Hill; 1 edition (February 1, 1997). ISBN 0-07-005489-4.
* Bollobas, Bela; ''Modern Graph Theory'', Springer; 1st edition (August 12, 2002). ISBN 0-387-98488-7.
* Zwillinger, Daniel; ''CRC Standard Mathematical Tables and Formulae'', Chapman & Hall/CRC; 31st edition (November 27, 2002). ISBN 1-58488-291-3.
 
[[Categoría:Categoría:Teoría de grafos]]
==External links==
* {{DADS|Self loop|selfloop}}
 
==See also==
* [[Cycle (graph theory)]]
* [[List of cycles]]
 
'''Loops in Topology'''
* [[Möbius ladder]]
* [[Möbius strip]]
* [[Strange loop]]
* [[Klein bottle]]
 
CATEGORÍA
 
[[en:Loop (graph theory)]]