Loop (graph theory)

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.