![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/d/d6/UndirectedDegrees_%2528Loop%2529.svg/640px-UndirectedDegrees_%2528Loop%2529.svg.png&w=640&q=50)
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
is denoted by
, and is the maximum of
's vertices' degrees. The minimum degree of a graph is denoted by
, and is the minimum of
's vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d6/UndirectedDegrees_%28Loop%29.svg/220px-UndirectedDegrees_%28Loop%29.svg.png)
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]