## Degree of Vertex

The degree of vertex is the total number of vertices in the graph minus 1 or we can say that the number of vertices adjacent to a vertex V is the degree of vertex.

1 2 3 |
Notation - deg(V). |

## Degree of vertex can be considered under two cases of graphs:

- Directed Graph
- Undirected Graph

### Directed Graph

A directed graph or digraph is a pair (V, E), where V is the vertex set and E is the set of vertex pairs as in “usual” graphs. The graph in which each vertex has its indegree and outdegree is known as directed graph.

Indegree of vertex V is the number of edges which are coming towards the vertex V.

1 2 3 4 |
Notation - deg<sup>-</sup>(V). |

**Outdegree of vertex** V is the number of edges which are going away from the vertex V.

1 2 3 4 |
Notation − deg<sup>+</sup>(V). |

**For example :**

Indegree of (a) -1

Outdegree of (a) – 2

### Undirected Graph

The graph in which there is no directed edges is known as undirected graph.

**For example:**

deg(a) = 2 there are 2 edges meeting at ‘a’

deg(b) = 3 there are 3 edges meeting at ‘b’

deg(d) = 2 there are 2 edges meeting at ‘d’

## Types of directed graph

**Symmetric directed graphs:**The graph in which all the edges are bidirected is called as symmetric directed graph.**Simple directed graph:**The directed graph that is without loops is called as simple directed graph.**Loop directed graph:**The directed graph that has loops is called as loop directed graph or loop digraph.**Complete directed graph:**When each pair of vertices of the simple directed graph is joined by a symmetric pair of directed arrows, this graph is called as complete directed graph.**Oriented graphs:**The directed graph that has no bidirected edges is called as oriented graph.**Weighted directed graph:**The directed graph in which weight is assigned to the directed arrows is called as weighted graph.

### For example:

**Flow networks:** These are the weighted graphs in which the two nodes are differentiated as source and sink.

**Rooted directed graph:** These are the directed graphs in which vertex is distinguished as root.

**Signal flow graphs:** The directed graph in which system variable is represented by nodes and connection between pairs and nodes is represented by branches are called as signal flow graphs.