# C++ Program to Generate a Random UnDirected Graph for a Given Number of Edges

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This is a C++ program to create a random graph using random edge generation.

Problem Description

1. This algorithm generates a undirected random graph for some random number of edges and vertexes.
2. The time complexity of this algorithm is O(v*e).

Problem Solution

1. This algorithm randomly assigns a number of vertexes and edges of the graph.
2. It connects vertexes randomly and generates cyclic, acyclic or disconnected undirected graphs.

Program/Source Code

C++ Program to create a random graph using random edge generation.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

#include<iostream>
#include<stdlib.h>

using namespace std;

// A function to generate random graph.
void GenerateRandGraphs(int NOE, int NOV)
{
int i, j, edge[NOE][2], count;
i = 0;
// Build a connection between two random vertex.
while(i < NOE)
{
edge[i][0] = rand()%NOV+1;
edge[i][1] = rand()%NOV+1;

if(edge[i][0] == edge[i][1])
continue;
else
{
for(j = 0; j < i; j++)
{
if((edge[i][0] == edge[j][0] && edge[i][1] == edge[j][1]) || (edge[i][0] == edge[j][1] && edge[i][1] == edge[j][0]))
i--;
}
}
i++;
}

// Print the random graph.
cout<<"\nThe generated random random graph is: ";
for(i = 0; i < NOV; i++)
{
count = 0;
cout<<"\n\t"<<i+1<<"-> { ";
for(j = 0; j < NOE; j++)
{
if(edge[j][0] == i+1)
{
cout<<edge[j][1]<<"   ";
count++;
}
else if(edge[j][1] == i+1)
{
cout<<edge[j][0]<<"   ";
count++;
}
else if(j == NOE-1 && count == 0)
cout<<"Isolated Vertex!";
}
cout<<" }";
}
}

int main()
{
int n, i, e, v;

cout<<"Random graph generation: ";

// Randomly assign vertex and edges of the graph.
v = 11+rand()%10;
cout<<"\nThe graph has "<<v<<" vertexes.";
e = rand()%((v*(v-1))/2);
cout<<"\nThe graph has "<<e<<" edges.";

// A function to generate a random undirected graph with e edges and v vertexes.
GenerateRandGraphs(e, v);
}
Program Explanation

1. Using rand(), assign random values to the number of vertex and edges of the graph.
2. Call GenerateRandGraphs(), with ‘e’ as the number of edges and ‘v’ as the number of vertexes, in the argument list.
3. Inside GenerateRandGraphs(), generate a connection between two random numbers.
4. Check for the self-edge and multiple edges between two vertexes.
5. Print all the connection of each vertex, irrespective of the direction.
6. Print “Isolated vertex” for the vertex having zero degrees.
7. Exit.

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Runtime Test Cases
Case 1:
Random graph generation:
The graph has 12 vertexes.
The graph has 53 edges.
The generated random random graph is:
1-> { 4   11   9   7   10   6   12   5   8   3    }
2-> { 4   12   11   3   7   9    }
3-> { 8   10   12   7   5   11   2   6   1    }
4-> { 2   1   12   11   10   9   8   5    }
5-> { 11   6   10   12   3   9   1   4    }
6-> { 5   11   10   7   1   8   9   3   12    }
7-> { 12   8   3   10   1   6   11   2    }
8-> { 3   12   7   10   9   6   1   4    }
9-> { 11   10   12   1   5   4   8   2   6    }
10-> { 3   9   5   8   11   12   7   6   1   4    }
11-> { 5   9   10   2   1   3   6   7   4   12    }
12-> { 2   3   7   8   4   9   10   5   1   11   6    }

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