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.

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): In a graph with one vertex, all edges must be loops.

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.