- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

It is the number of vertices adjacent to a vertex V.

**Notation** − deg(V).

In a simple graph with n number of vertices, the degree of any vertices is −

deg(v) = n – 1 ∀ v ∈ G

A vertex can form an edge with all other vertices except by itself. So the degree of a vertex will be up to the **number of vertices in the graph minus 1**. This 1 is for the self-vertex as it cannot form a loop by itself. If there is a loop at any of the vertices, then it is not a Simple Graph.

Degree of vertex can be considered under two cases of graphs −

- Undirected Graph
- Directed Graph

An undirected graph has no directed edges. Consider the following examples.

Take a look at the following graph −

In the above Undirected Graph,

deg(a) = 2, as there are 2 edges meeting at vertex 'a'.

deg(b) = 3, as there are 3 edges meeting at vertex 'b'.

deg(c) = 1, as there is 1 edge formed at vertex 'c'

So 'c' is a

**pendent vertex**.deg(d) = 2, as there are 2 edges meeting at vertex 'd'.

deg(e) = 0, as there are 0 edges formed at vertex 'e'.

So 'e' is an

**isolated vertex**.

Take a look at the following graph −

In the above graph,

deg(a) = 2, deg(b) = 2, deg(c) = 2, deg(d) = 2, and deg(e) = 0.

The vertex 'e' is an isolated vertex. The graph does not have any pendent vertex.

In a directed graph, each vertex has an **indegree** and an **outdegree**.

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

**Notation**− deg^{−}(V).

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

**Notation**− deg^{+}(V).

Consider the following examples.

Take a look at the following directed graph. Vertex 'a' has two edges, 'ad' and 'ab', which are going outwards. Hence its outdegree is 2. Similarly, there is an edge 'ga', coming towards vertex 'a'. Hence the indegree of 'a' is 1.

The indegree and outdegree of other vertices are shown in the following table −

Vertex | Indegree | Outdegree |
---|---|---|

a | 1 | 2 |

b | 2 | 0 |

c | 2 | 1 |

d | 1 | 1 |

e | 1 | 1 |

f | 1 | 1 |

g | 0 | 2 |

Take a look at the following directed graph. Vertex 'a' has an edge 'ae' going outwards from vertex 'a'. Hence its outdegree is 1. Similarly, the graph has an edge 'ba' coming towards vertex 'a'. Hence the indegree of 'a' is 1.

The indegree and outdegree of other vertices are shown in the following table −

Vertex | Indegree | Outdegree |
---|---|---|

a | 1 | 1 |

b | 0 | 2 |

c | 2 | 0 |

d | 1 | 1 |

e | 1 | 1 |

- Related Questions & Answers
- Pendent Vertex, Isolated Vertex and Adjacency of a graph
- Cut Set and Cut Vertex of Graph
- C++ Program to Find the Vertex Connectivity of a Graph
- C++ Program to Implement a Heuristic to Find the Vertex Cover of a Graph
- C++ program to find minimum vertex cover size of a graph using binary search
- C++ Program to Generate a Graph for a Given Fixed Degree Sequence
- Degree of an Array in C++
- Properties of a Graph
- Transitive closure of a Graph
- Complement of Graph
- Connectivity of Graph
- Types of Graph
- Finding degree of subarray in an array JavaScript
- Vertex Covering
- Finding the vertex, focus and directrix of a parabola in C++

Advertisements