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In graph theory, the degree 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. The degree of a vertex v {\displaystyle v} is denoted deg {\displaystyle \deg} or deg v {\displaystyle \deg v}. The maximum degree of a graph G {\displaystyle G} , denoted by Δ {\displaystyle \Delta } , and the minimum degree of a graph, denoted by δ {\displaystyle \delta } , 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.
In a regular graph, every vertex has the same degree, and so we can speak of the degree of the graph. A complete graph is a special kind of regular graph where all vertices have the maximum possible degree, n − 1 {\displaystyle n-1}.
In a signed graph, the number of positive edges connected to the vertex v {\displaystyle v} is called positive deg {\displaystyle } and the number of connected negative edges is entitled negative deg {\displaystyle }.