{{Short description|Edge that connects a node to itself}} thumb|A graph with a loop on vertex 1
In graph theory, a '''loop''' (also called a '''self-loop''' or a ''buckle'') is an edge that connects a vertex to itself. A simple graph contains no loops.
Depending on the context, a 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): * Where graphs are defined so as to ''allow'' loops and multiple edges, a graph without loops or multiple edges is often distinguished from other graphs by calling it a ''simple graph''. * Where graphs are defined so as to ''disallow'' loops and multiple edges, a graph that does have loops or multiple edges is often distinguished from the graphs that satisfy these constraints by calling it a ''multigraph'' or ''pseudograph''.
In a graph with one vertex, all edges must be loops. Such a graph is called a bouquet.
==Degree== For an undirected graph, the degree of a vertex is equal to the number of adjacent vertices.
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.
For a directed graph, a loop adds one to the in degree and one to the out degree.
==See also== ===In graph theory=== * Cycle (graph theory) * Graph theory * Glossary of graph theory
===In topology=== * Möbius ladder * Möbius strip * Strange loop * Klein bottle
==References== {{reflist}}
* Balakrishnan, V. K.; ''Graph Theory'', McGraw-Hill; 1 edition (February 1, 1997). {{isbn|0-07-005489-4}}. * Bollobás, Béla; ''Modern Graph Theory'', Springer; 1st edition (August 12, 2002). {{isbn|0-387-98488-7}}. * Diestel, Reinhard; ''Graph Theory'', Springer; 2nd edition (February 18, 2000). {{isbn|0-387-98976-5}}. * Gross, Jonathon L, and Yellen, Jay; ''Graph Theory and Its Applications'', CRC Press (December 30, 1998). {{isbn|0-8493-3982-0}}. * Gross, Jonathon L, and Yellen, Jay; (eds); ''Handbook of Graph Theory''. CRC (December 29, 2003). {{isbn|1-58488-090-2}}. * Zwillinger, Daniel; ''CRC Standard Mathematical Tables and Formulae'', Chapman & Hall/CRC; 31st edition (November 27, 2002). {{isbn|1-58488-291-3}}.
==External links== * {{DADS|Self loop|selfloop}}
Category:Graph theory objects