A graph G,consists of two sets V and E. V is a finite non-empty set of vertices.E is a set of pairs of vertices,these pairs are called as edges V(G) and E(G) will represent the sets of vertices and edges of graph G.

Undirected graph – It is a graph with V vertices and E edges where E edges are undirected. In undirected graph, each edge which is present between the vertices V_{i} and V_{j},is represented by using a pair of round vertices (Vi,Vj).

Directed graph – It is a graph with V vertices and E edges where E edges are directed.In directed graph,if V_{i} and V_{j} nodes having an edge.than it is represented by a pair of triangular brackets V_{i},V_{j}.

Here is the source code of the C program to create a graph using adjacency matrix. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

`//... A Program to represent a Graph by using an Adjacency Matrix method`

`#include <stdio.h>`

`#include <stdlib.h>`

void main()

`{`

int option;

`do`

`{`

printf("\n A Program to represent a Graph by using an ");

printf("Adjacency Matrix method \n ");

printf("\n 1. Directed Graph ");

printf("\n 2. Un-Directed Graph ");

printf("\n 3. Exit ");

printf("\n\n Select a proper option : ");

scanf("%d", &option);

switch(option)

`{`

case 1 : dir_graph();

break;

case 2 : undir_graph();

break;

case 3 : exit(0);

} // switch

}while(1);

`}`

int dir_graph()

`{`

int adj_mat[50][50];

int n;

int in_deg, out_deg, i, j;

printf("\n How Many Vertices ? : ");

scanf("%d", &n);

read_graph(adj_mat, n);

printf("\n Vertex \t In_Degree \t Out_Degree \t Total_Degree ");

for (i = 1; i <= n ; i++ )

`{`

in_deg = out_deg = 0;

for ( j = 1 ; j <= n ; j++ )

`{`

if ( adj_mat[j][i] == 1 )

`in_deg++;`

`}`

for ( j = 1 ; j <= n ; j++ )

if (adj_mat[i][j] == 1 )

`out_deg++;`

printf("\n\n %5d\t\t\t%d\t\t%d\t\t%d\n\n",i,in_deg,out_deg,in_deg+out_deg);

`}`

return;

`}`

int undir_graph()

`{`

int adj_mat[50][50];

int deg, i, j, n;

printf("\n How Many Vertices ? : ");

scanf("%d", &n);

read_graph(adj_mat, n);

printf("\n Vertex \t Degree ");

for ( i = 1 ; i <= n ; i++ )

`{`

deg = 0;

for ( j = 1 ; j <= n ; j++ )

if ( adj_mat[i][j] == 1)

`deg++;`

printf("\n\n %5d \t\t %d\n\n", i, deg);

`}`

return;

`}`

int read_graph ( int adj_mat[50][50], int n )

`{`

int i, j;

char reply;

for ( i = 1 ; i <= n ; i++ )

`{`

for ( j = 1 ; j <= n ; j++ )

`{`

if ( i == j )

`{`

adj_mat[i][j] = 0;

continue;

`}`

printf("\n Vertices %d & %d are Adjacent ? (Y/N) :",i,j);

scanf("%c", &reply);

if ( reply == 'y' || reply == 'Y' )

adj_mat[i][j] = 1;

`else`

adj_mat[i][j] = 0;

`}`

`}`

return;

`}`

$ gcc graph.c -o graph $ ./graph A Program to represent a Graph by using an Adjacency Matrix method 1. Directed Graph 2. Un-Directed Graph 3. Exit Select a proper option : How Many Vertices ? : Vertices 1 & 2 are Adjacent ? (Y/N) : N Vertices 1 & 3 are Adjacent ? (Y/N) : Y Vertices 1 & 4 are Adjacent ? (Y/N) : Y Vertices 2 & 1 are Adjacent ? (Y/N) : Y Vertices 2 & 3 are Adjacent ? (Y/N) : Y Vertices 2 & 4 are Adjacent ? (Y/N) : N Vertices 3 & 1 are Adjacent ? (Y/N) : Y Vertices 3 & 2 are Adjacent ? (Y/N) : Y Vertices 3 & 4 are Adjacent ? (Y/N) : Y Vertices 4 & 1 are Adjacent ? (Y/N) : Y Vertices 4 & 2 are Adjacent ? (Y/N) : N Vertices 4 & 3 are Adjacent ? (Y/N) : Y Vertex In_Degree Out_Degree Total_Degree 1 2 0 2 2 1 2 3 3 0 1 1 4 1 1 2 A Program to represent a Graph by using an Adjacency Matrix method 1. Directed Graph 2. Un-Directed Graph 3. Exit

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