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Degree (graph theory)

Number of edges touching a vertex in a graph / From Wikipedia, the free encyclopedia

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In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge.[1] The degree of a vertex is denoted or . The maximum degree of a graph , denoted by , and the minimum degree of a graph, denoted by , are the maximum and minimum of its vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0.

UndirectedDegrees_%28Loop%29.svg
A graph with a loop having vertices labeled by degree

In a regular graph, every vertex has the same degree, and so we can speak of the degree of the graph. A complete graph (denoted , where is the number of vertices in the graph) is a special kind of regular graph where all vertices have the maximum possible degree, .

In a signed graph, the number of positive edges connected to the vertex is called positive deg and the number of connected negative edges is entitled negative deg.[2][3]

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