### Write a program, which given inputs as integer pairs representing edges, creates an adjacency matrix for a graph.

**Source Code**

Brief explanation is provided after the source code.

#include <stdio.h> #include <stdlib.h> #define V 8 int main(void){ int i, j, a, adj[V][V]; for(i = 0; i < V; i++) for(j = 0; j < V; j++) adj[i][j] = 0; /* initialize matrix */ for(i = 0; i < V; i++) adj[i][i] = 1; /* major diagonal */ /* Now read in edges as vertex pairs */ printf("\nEnter vertex pairs - Press to end\n"); while(scanf("%d%d", &i, &j) == 2) { adj[i][j] = 1; adj[j][i] = 1; } /* display matrix */ for(i = 0; i < V; i++) if(i == 0) printf("%6d", i); /* 1st column label indented */ else printf("%3d", i); /* other column labels */ printf("\n"); for(i = 0; i < V; i++){ printf("%3d", i); /* row label*/ for(j = 0; j < V; j++) printf("%3d", adj[i][j]); printf("\n"); } return 0; }

When you compile and execute the above program it produces the following result on Linux:

Enter vertex pairs - Press to end 0 1 3 4 6 7 9 8 12 4 5 0 2 4 6 17 0 1 2 3 4 5 6 7 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 2 0 0 1 0 1 0 0 0 3 0 0 0 1 1 0 0 0 4 0 0 1 1 1 0 0 0 5 1 0 0 0 1 1 0 0 6 0 0 0 0 0 0 1 1 7 0 0 0 0 0 0 1 1

**Brief Explanation**

- An adjacency matrix is a 2-D matrix used to represent a graph. One can tell if there is an edge between vertex i and vertex j by checking the cell at the intersection of row i and column j: if it contains 1, there is an edge between the vertices; if it is zero, there is no edge between the vertices.
- From the result of the program, the cell at the intersection of each of the vertex pairs provided contains 1 which means there is an edge between the vertices.
- For an undirected graph, the matrix is symmetrical about the major diagonal because the entry at cell[i][j] is the same entry in cell [j][i]. By convention, the major diagonal cells are assigned the value 1 (each vertex is connected to itself).