Given the edges of a graph as a list of tuples, construct an adjacency matrix to represent the graph in Python.

Examples:

Input:
V = 3 (Number of vertices)
edges = [(0, 1), (1, 2), (2, 0)]

Output:

[ [0, 1, 1],

[1, 0, 1],

[1, 1, 0]]

Input:
V = 4 (Number of vertices)
edges = [(0, 1), (1, 2), (1, 3), (2, 3), (3, 0)]

Output:

[ [0, 1, 0, 1],

[1, 0, 1, 1],

[0, 1, 0, 1],

[1, 1, 1, 0]]

step-by-step algorithm:

1. Initialize an empty V×V matrix with all zeros.
2. For each edge (u,v) in the given list of edges, set matrix[u][v] = 1 and matrix[v][u] = 1 (since the graph is undirected).

Below is the implementation of the algorithm:

def create_adjacency_matrix(V, edges):
    # Initialize an empty V x V matrix with all zeros
    matrix = [[0] * V for _ in range(V)]
    
    # Populate the matrix based on the edges
    for edge in edges:
        u, v = edge
        matrix[u][v] = 1
        matrix[v][u] = 1  # Undirected graph
    
    return matrix


# Example 1
V1 = 3
edges1 = [(0, 1), (1, 2), (2, 0)]
adj_matrix1 = create_adjacency_matrix(V1, edges1)
for row in adj_matrix1:
    print(row)
print()

# Example 2
V2 = 4
edges2 = [(0, 1), (1, 2), (1, 3), (2, 3), (3, 0)]
adj_matrix2 = create_adjacency_matrix(V2, edges2)
for row in adj_matrix2:
    print(row)

[0, 1, 1]
[1, 0, 1]
[1, 1, 0]

[0, 1, 0, 1]
[1, 0, 1, 1]
[0, 1, 0, 1]
[1, 1, 1, 0]

Time Complexity: O(V+E), where V is the number of vertices and E is the number of edges.
Auxiliary Space: O(V^2)