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Loop (graph theory) : ウィキペディア英語版
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".
==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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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