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# C program to implement Adjacency Matrix of a given Graph

Given a undirected Graph of N vertices 1 to N and M edges in form of 2D array arr[][] whose every row consists of two numbers X and Y which denotes that there is a edge between X and Y, the task is to write C program to create Adjacency Matrix of the given Graph. Examples:

Input: N = 5, M = 4, arr[][] = { { 1, 2 }, { 2, 3 }, { 4, 5 }, { 1, 5 } } Output: 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 Input: N = 3, M = 4, arr[][] = { { 1, 2 }, { 2, 3 }, { 3, 1 }, { 2, 2 } } Output: 0 1 1 1 1 1 1 1 0

Approach: The idea is to use a square Matrix of size NxN to create Adjacency Matrix. Below are the steps:

1. Create a 2D array(say Adj[N+1][N+1]) of size NxN and initialise all value of this matrix to zero.
2. For each edge in arr[][](say X and Y), Update value at Adj[X][Y] and Adj[Y][X] to 1, denotes that there is a edge between X and Y.
3. Display the Adjacency Matrix after the above operation for all the pairs in arr[][].

Below is the implementation of the above approach:

## C

 `// C program for the above approach``#include ` `// N vertices and M Edges``int` `N, M;` `// Function to create Adjacency Matrix``void` `createAdjMatrix(``int` `Adj[][N + 1],``                     ``int` `arr[][2])``{` `    ``// Initialise all value to this``    ``// Adjacency list to zero``    ``for` `(``int` `i = 0; i < N + 1; i++) {` `        ``for` `(``int` `j = 0; j < N + 1; j++) {``            ``Adj[i][j] = 0;``        ``}``    ``}` `    ``// Traverse the array of Edges``    ``for` `(``int` `i = 0; i < M; i++) {` `        ``// Find X and Y of Edges``        ``int` `x = arr[i][0];``        ``int` `y = arr[i][1];` `        ``// Update value to 1``        ``Adj[x][y] = 1;``        ``Adj[y][x] = 1;``    ``}``}` `// Function to print the created``// Adjacency Matrix``void` `printAdjMatrix(``int` `Adj[][N + 1])``{` `    ``// Traverse the Adj[][]``    ``for` `(``int` `i = 1; i < N + 1; i++) {``        ``for` `(``int` `j = 1; j < N + 1; j++) {` `            ``// Print the value at Adj[i][j]``            ``printf``("%d ", Adj[i][j]);``        ``}``        ``printf``("\n");``    ``}``}` `// Driver Code``int` `main()``{` `    ``// Number of vertices``    ``N = 5;` `    ``// Given Edges``    ``int` `arr[][2]``        ``= { { 1, 2 }, { 2, 3 },``            ``{ 4, 5 }, { 1, 5 } };` `    ``// Number of Edges``    ``M = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``// For Adjacency Matrix``    ``int` `Adj[N + 1][N + 1];` `    ``// Function call to create``    ``// Adjacency Matrix``    ``createAdjMatrix(Adj, arr);` `    ``// Print Adjacency Matrix``    ``printAdjMatrix(Adj);` `    ``return` `0;``}`

Output:

```0 1 0 0 1
1 0 1 0 0
0 1 0 0 0
0 0 0 0 1
1 0 0 1 0```

Time Complexity: O(N^2), where N is the number of vertices in a graph.

Space Complexity: O(N^2), where N is the number of vertices.