Loop (graph theory)
In graph theory, a loop 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 :
- 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.
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.