Editing Loop (graph theory) (section)

{{Short description|Edge that connects a node to itself}}
[[Image:6n-graph2.svg|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 (graph theory)|edge]] that connects a [[vertex (graph theory)|vertex]] to itself. A [[simple graph]] contains no loops.

Depending on the context, a [[Graph (discrete 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):
* 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 graph|bouquet]].