# C++ Program to Construct a Random Graph by the Method of Random Edge Selection

C++Server Side ProgrammingProgramming

In this program a random graph is generated for random vertices and edges. The time complexity of this program is O(v*e). Where v is the number of vertices and e is the number of edges.

## Algorithm

Begin
Develop a function GenRandomGraphs(), with ‘e’ as the
number of edges and ‘v’ as the number of vertexes, in the argument list.
Assign random values to the number of vertex and edges of the graph, Using rand() function.
Print the connections of each vertex, irrespective of the direction.
Print “Isolated vertex” for the vertex having no degree.
End

## Example

#include<iostream>
#include<stdlib.h>
using namespace std;
void GenRandomGraphs(int NOEdge, int NOVertex) {
int i, j, edge[NOEdge], count;
i = 0;
//Assign random values to the number of vertex and edges of the graph, Using rand().
while(i < NOEdge) {
edge[i] = rand()%NOVertex+1;
edge[i] = rand()%NOVertex+1;
//Print the connections of each vertex, irrespective of the direction.
if(edge[i] == edge[i])
continue;
else {
for(j = 0; j < i; j++) {
if((edge[i] == edge[j] && edge[i] == edge[j]) || (edge[i] == edge[j] && edge[i] == edge[j]))i--;
}
}
i++;
}
cout<<"\nThe generated random graph is: ";
for(i = 0; i < NOVertex; i++) {
count = 0;
cout<<"\n\t"<<i+1<<"-> { ";
for(j = 0; j < NOEdge; j++) {
if(edge[j] == i+1) {
cout<<edge[j]<<" ";
count++;
} else if(edge[j] == i+1) {
cout<<edge[j]<<" ";
count++;
} else if(j== NOEdge-1&& count == 0)cout<<"Isolated Vertex!";
//Print “Isolated vertex” for the vertex having no degree.
}
cout<<" }";
}
}
int main() {
int i, e, n;
cout<<"Random graph generation: ";
n= 7 + rand()%6;
cout<<"\nThe graph has "<<n<<" vertices";
e = rand()%((n*(n-1))/2);
cout<<"\nand has "<<e<<" edges.";
GenRandomGraphs(e, n);
}

## Output

Random graph generation:
The graph has 8 vertices
and has 18 edges.
The generated random graph is:
1-> { 5 4 2 }
2-> { 4 8 6 3 1 5 }
3-> { 5 4 7 2 }
4-> { 2 3 7 1 8 5 }
5-> { 3 1 7 4 2 8 }
6-> { 2 8 7 }
7-> { 4 3 5 6 }
8-> { 2 6 4 5 }