Add and Remove Edge in Adjacency Matrix representation of a Graph

Prerequisites: Graph and its representations
Given an adjacency matrix g[][] of a graph consisting of N vertices, the task is to modify the matrix after insertion of all edges[] and removal of edge between vertices (X, Y). In an adjacency matrix, if an edge exists between vertices i and j of the graph, then g[i][j] = 1 and g[j][i] = 1. If no edge exists between these two vertices, then g[i][j] = 0 and g[j][i] = 0.

Examples:

Input: N = 6, Edges[] = {{0, 1}, {0, 2}, {0, 3}, {0, 4}, {1, 3}, {2, 3}, {2, 4}, {2, 5}, {3, 5}}, X = 2, Y = 3 
Output: 
Adjacency matrix after edge insertion:
0 1 1 1 1 0 
1 0 0 1 0 0 
1 0 0 1 1 1 
1 1 1 0 0 1 
1 0 1 0 0 0 
0 0 1 1 0 0
Adjacency matrix after edge removal:
0 1 1 1 1 0 
1 0 0 1 0 0 
1 0 0 0 1 1 
1 1 0 0 0 1 
1 0 1 0 0 0 
0 0 1 1 0 0 
Explanation: 
The graph and the corresponding adjacency matrix after insertion of edges:

👁 Image

The graph after removal and adjacency matrix after removal of edge between vertex X and Y:

👁 Image

Input: N = 6, Edges[] = {{0, 1}, {0, 2}, {0, 3}, {0, 4}, {1, 3}, {2, 3}, {2, 4}, {2, 5}, {3, 5}}, X = 3, Y = 5 
Output: 
Adjacency matrix after edge insertion:
0 1 1 1 1 0 
1 0 0 1 0 0 
1 0 0 1 1 1 
1 1 1 0 0 1 
1 0 1 0 0 0 
0 0 1 1 0 0
Adjacency matrix after edge removal:
0 1 1 1 1 0 
1 0 0 1 0 0 
1 0 0 1 1 1 
1 1 1 0 0 0 
1 0 1 0 0 0 
0 0 1 0 0 0

Approach: 
Initialize a matrix of dimensions N x N and follow the steps below:

• Inserting an edge: To insert an edge between two vertices suppose i and j, set the corresponding values in the adjacency matrix equal to 1, i.e. g[i][j]=1 and g[j][i]=1 if both the vertices i and j exists.
• Removing an edge: To remove an edge between two vertices suppose i and j, set the corresponding values in the adjacency matrix equal to 0. That is, set g[i][j]=0 and g[j][i]=0 if both the vertices i and j exists.

Below is the implementation of the above approach:

Adjacency matrix after edge insertions:

 0 1 1 1 1 0
 1 0 0 1 0 0
 1 0 0 1 1 1
 1 1 1 0 0 1
 1 0 1 0 0 0
 0 0 1 1 0 0
Adjacency matrix after edge removal:

 0 1 1 1 1 0
 1 0 0 1 0 0
 1 0 0 0 1 1
 1 1 0 0 0 1
 1 0 1 0 0 0
 0 0 1 1 0 0

Time Complexity: Insertion and Deletion of an edge requires O(1) complexity while it takes O(N²) to display the adjacency matrix. 
Auxiliary Space: O(N²)