Loop (graph theory)

Graph with loop in the first node.

A loop or loop is an edge that connects a node to itself in graph theory. A graph without loops is called a grindless or grind-free graph.

Depending on the context, graphs or multigraphs can be defined to allow or exclude loops (often in conjunction with multiple-edge permissions): Edit grading source text

For an undirected graph, the degree of a node is equal to the number of adjacent nodes.

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

For a directed graph, a loop increases the input and output levels of a node by one unit. Edit source text

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