In graph theory, the degree (or valency) of a vertex is the number of edges incident to the vertex. The degree of a vertex v is denoted deg(v). A labeled graph with 6 vertices and 7 edges. ... This article just presents the basic definitions. ... This article just presents the basic definitions. ... A graph with 6 vertices (nodes) and 7 edges. ...

Undirected graphs

A graph with 6 vertices and 7 edges

For an undirected graph, the degree of a vertex is the number of edges incident to the vertex. This means that each loop is counted twice. This is because each edge has two endpoints and each endpoint adds to the degree. Image File history File links 6n-graf. ... Image File history File links 6n-graf. ... This article just presents the basic definitions. ... A graph with 6 vertices (nodes) and 7 edges. ...

The graph shown to the right has the following degrees:

Directed graphs

A directed graph with 4 vertices and 5 edges

In a directed graph, an edge has two distinct ends: a head (the end with an arrow) and a tail. Each end is counted separately. The sum of head endpoints count toward the indegree and the sum of tail endpoints count toward the outdegree. Image File history File links Directed_graph. ... Image File history File links Directed_graph. ... This article just presents the basic definitions. ...

The indegree is denoted deg ⁺ (v) and the outdegree as deg ⁻ (v)

The image to the right has the following degrees:

Special cases of degree value

Isolated vertex

If a vertex has a zero degree then it is called an isolated vertex. An isolated vertex of a graph is a vertex that has degree zero in the graph, i. ...

Leaf vertex

An undirected graph with leaf nodes 4, 5, 6, 7, 10, 11, and 12

If a vertex has a unity degree then it is a leaf. This is fairly common in trees in graph theory and trees in data structures. Image File history File links Depth-first-tree. ... Image File history File links Depth-first-tree. ... A labeled tree with 6 vertices and 5 edges In graph theory, a tree is a graph in which any two vertices are connected by exactly one path. ... In computer science, a tree is a widely-used computer data structure that emulates a tree structure with a set of linked nodes. ... A binary tree, a simple type of branching linked data structure. ...

Regular graph

If each vertex of the graph has the same degree k the graph is called a k-regular graph and the graph itself is said to have degree k. In graph theory, a regular graph is a graph where each vertex has the same number of neighbors, i. ...

Source

A vertex with deg ⁺ (v) = 0 is called a source. This name comes from the fact that the node is the origin/source of all of its incident edges. In the image under #Directed graphs, vertex 1 is a source node.

Sink

A vertex with deg ⁻ (v) = 0 is called a sink. Similarly to source nodes, a sink gets its name from the fact that the node is the termination/destination/sink of all of its incident edges. In the image under #Directed graphs, vertex 2 is a sink node.

Euler tour

A graph is Eulerian if and only if every vertex is of even degree. Bridges of Königsberg corresponding graph In the mathematical field of graph theory an Eulerian path is a path in a graph which visits each edge exactly once. ...

Some theorems

The degree sum formula states that, given a graph G = (V,E), The degree sum formula is a fundamental theorem of graph theory which states that, given a graph G=(V,E), The formula implies that in any graph, the number of vertices with odd degree is even. ...

since each edge is incident to two vertices. The formula implies that in any graph, the number of vertices with odd degree is even.