Loop (graph theory)

As a loop or noose is called an edge in graph theory, which connects a node to itself. A graph without loops is called loop -free or loop- free graph.

Depending on the context graph or multigraph can be defined such that they allow loops or exclude (often in conjunction with the approval of multiple edges ):

• Allowed to loops or multiple edges in the definition of the graph to the graph without loops and multiple edges are referred to as a simple distinction graph.
• By connecting loops or multiple edges in the definition of graphs from graphs with loops and multiple edges to distinguish are called " multigraph ".

Number of degrees

In a non-directional graph of the degree of a node is equal to the number of neighbor nodes.

The loop is a special case, because it increases the number of degrees of a node by two. The node is thus counted twice as its own neighbor.

In a directed graph a loop increases the input and output degree of a node in each case by one unit.