- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Matrix Representation of Graphs
A graph can be represented using Adjacency Matrix way.
Adjacency Matrix
An Adjacency Matrix A[V][V] is a 2D array of size V × V where $V$ is the number of vertices in a undirected graph. If there is an edge between Vx to Vy then the value of A[Vx][Vy]=1 and A[Vy][Vx]=1, otherwise the value will be zero.
For a directed graph, if there is an edge between Vx to Vy, then the value of A[Vx][Vy]=1, otherwise the value will be zero.
Adjacency Matrix of an Undirected Graph
Let us consider the following undirected graph and construct the adjacency matrix −
Adjacency matrix of the above undirected graph will be −
a | b | c | d | |
a | 0 | 1 | 1 | 0 |
b | 1 | 0 | 1 | 0 |
c | 1 | 1 | 0 | 1 |
d | 0 | 0 | 1 | 0 |
Adjacency Matrix of a Directed Graph
Let us consider the following directed graph and construct its adjacency matrix −
Adjacency matrix of the above directed graph will be −
a | b | c | d | |
a | 0 | 1 | 1 | 0 |
b | 0 | 0 | 1 | 0 |
c | 0 | 0 | 0 | 1 |
d | 0 | 0 | 0 | 0 |