Adjacency Matrices and their properties

MathematicsComputer EngineeringMCA

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 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 undirected

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 directed

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