Adjacency Matrices and their properties

Adjacency Matrix

Adjacency Matrix is used to represent a graph. We can represent directed as well as undirected graphs using adjacency matrices. Following are the key properties of an Adjacency matrix.

Properties

• 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 V_x to V_y then the value of A[V_x][V_y] = 1 and A[V_y][V_x]=1, otherwise the value will be zero.

• For a directed graph, if there is an edge between V_x to V_y, then the value of A[V_x][V_y]=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 −

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 −

Mahesh Parahar

Published on 22-Aug-2019 12:07:08

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