# 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 $v$ is denoted $\deg(v)$ or $\deg v$. The **maximum degree** of a graph $G$, denoted by $\Delta (G)$, and the **minimum degree** of a graph, denoted by $\delta (G)$, 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 (denoted $K_{n}$, where $n$ is the number of vertices in the graph) is a special kind of regular graph where all vertices have the maximum possible degree, $n-1$.

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

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