Discrete Mathematics : In-Degree & Out-Degree of a Vertex

In this section of In-Degree & Out-Degree of a Vertex, we cover the chapter "Graph Theory". Here we explain how to find the indegree and out degree of a vertex in a graph.

In Degree of a Vertex: The In-degree of a vertex v written by deg(v), is the number of edges with v as the terminated vertex. To find the in-degree of a vertex, just count the number of edges ends at the vertex.

Out Degree of a Vertex: The Out-degree of a vertex v written by deg+(v), is the number of edges with v as the initial vertex. To find the on-degree of a vertex, just count the number of edges starting from the vertex.

Therefore the degree of a vertex is equal to the sum of In-Degree of a vertex and the Out-Degree of a vertex i.e.

Deg(v) = deg(v) + deg+(v)

Example: Find the In -Degree, Out-degree, and degree of each vertex of a graph given below.

In-degree and out degree of a vertex
The In-Degree and Out-Degree of each vertex in a graph is

In-Degree of a vertex 'v1' = deg(v1) = 1 and Out-Degree of a vertex 'v1' = deg(v1) = 2
In-Degree of a vertex 'v2' = deg(v2) = 1 and Out-Degree of a vertex 'v2' = deg(v2) = 3
In-Degree of a vertex 'v3' = deg(v3) = 1 and Out-Degree of a vertex 'v3' = deg(v3) = 2
In-Degree of a vertex 'v4' = deg(v4) = 5 and Out-Degree of a vertex 'v4' = deg(v4) = 0
In-Degree of a vertex 'v5' = deg(v5) = 1 and Out-Degree of a vertex 'v5' = deg(v5) = 2
In-Degree of a vertex 'v6' = deg(v6) = 0 and Out-Degree of a vertex 'v6' = deg(v6) = 0

And by the definition, the degree of a vertex is Deg(v) = deg(v) + deg+(v). Therefore,

Degree of a vertex 'v1' = deg(v1) = 1 + 2 = 3
Degree of a vertex 'v2' = deg(v2) = 1 + 3 = 4
Degree of a vertex 'v3' = deg(v3) = 1 + 2 = 3
Degree of a vertex 'v4' = deg(v4) = 5 + 0 = 5
Degree of a vertex 'v5' = deg(v5) = 1 + 2 = 3
Degree of a vertex 'v6' = deg(v6) = 0 + 0 = 0

Try it : Find the In -Degree, Out-degree, and degree of each vertex of a graph given below.

degree of a vertex exampleand In and out degree example graph