Representation of Graphs

MathematicsComputer EngineeringMCA

There are mainly two ways to represent a graph −

  • Adjacency Matrix
  • Adjacency List

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. And 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 −

The 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 −

The 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

Adjacency List

In the adjacency list, an array (A[V]) of linked lists is used to represent the graph G with V number of vertices. An entry A[Vx] represents the linked list of vertices adjacent to the Vx-th vertex. The adjacency list of the undirected graph is as shown in the figure below −


raja
Published on 26-Aug-2019 06:42:17
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