# 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:

- Create a 2D array(say
**Adj[N+1][N+1]**) of size NxN and initialise all value of this matrix to zero. - 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. - Display the Adjacency Matrix after the above operation for all the pairs in
**arr[][]**.

Below is the implementation of the above approach:

`// C program for the above approach` `#include <stdio.h>` ` ` `// 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.

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