ADJACENT MATRIX

 This usually used in representation of graphs.If there are n vertices in graph then there are  n rows and n columns in matrix.

Let us take Ith row and Jth column then A[I][J] represents the edge between two nodes I  & J.If a[I][J] == 0 then there is no edge between node I and node J & if A[I][J] == 1 then there is edge.

These type of graph representation is used when there are more number of edges.Reason is that if there are e less number of edges then lot of space will wasted in storing the zeroes which is not good thing.

Following is the graph  and its adjancy matrix =>

    

#include<stdio.h>

#include<stdlib.h>

int main()

{

    // n is number of edges

    int n;

    printf("Enter the number of edges => ");

    scanf("%d",&n);

    // construct adjancy matrix

    int adjMatrix[n+1][n+1];

    // iterate for status of connected or not

    for (int i = 0; i < n; i++)

    {

        for(int j = 0; j < n;j++){

            printf("Are vertices %d & %d connected.1 yes and 0 for no",i,j);

            int key;

            scanf("%d",&key);

            adjMatrix[i][j] = key;

        }

    }

   

    // traverse for checking the connectivity

    for (int i = 0; i < n; i++)

    {

        for(int j = 0; j < n;j++){

            if (adjMatrix[i][j])

            {

                printf("%d & %d vertices are connected\n",i,j);

            }else{

                printf("%d & %d vertices are not connected\n",i,j);

            }

           

        }

    }

    return 0;

}

Enter the number of edges => 2 Are vertices 0 & 0 connected.1 yes and 0 for no1 Are vertices 0 & 1 connected.1 yes and 0 for no1 Are vertices 1 & 0 connected.1 yes and 0 for no1 Are vertices 1 & 1 connected.1 yes and 0 for no1 0 & 0 vertices are connected 0 & 1 vertices are connected 1 & 0 vertices are connected 1 & 1 vertices are connected