# Graph Representation using Incidence Matrix in C++

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This is a C++ program to represent graph using incidence matrix.

Problem Description

1. This algorithm represents a graph using incidence matrix.
2. The time complexity of this algorithm is O(v*v).

Problem Solution

1. This algorithm takes the input of the number of vertex.
2. For each pair of vertex ask user whether they are connected or not.
3. Print the incidence matrix.
4. Exit.

Program/Source Code

C++ program to represent graph using incidence matrix.
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

```#include<iostream>
#include<iomanip>

using namespace std;

// A function to print the incidence matrix.
void PrintMat(int mat[], int n, int count)
{
int i, j;

cout<<"\n\n"<<setw(6)<<"";
for(i = 0; i < n; i++)
cout<<setw(6)<<"V("<<i+1<<")";
cout<<"\n\n";

// Print the incidence matrix.
for(i = 0; i < count; i++)
{
cout<<setw(6)<<"E("<<i+1<<")";

for(j = 0; j < n; j++)
{
cout<<setw(6)<<mat[i][j];
}

cout<<"\n\n";
}
}

int main()
{
int i, j, v, k, count = 0, n, incimat;

cout<<"Enter the number of vertexes: ";
cin>>v;

// Take input of the adjacency of each pair of vertexes.
for(i = 0; i < v; i++)
{
for(j = i+1; j < v; j++)
{
cout<<"\nEnter 1 if the vertex "<<i+1<<" is adjacent to "<<j+1<<", otherwise 0: ";
cin>>n;
if(n == 1)
{
for(k = 0; k < v; k++)
{
if(k == i || k == j)
incimat[count][k] = 1;
else
incimat[count][k] = 0;
}
count++;
cout<<"\t\tIt is edge E("<<count<<").";
}
}
}

PrintMat(incimat, v, count);
}```
Program Explanation

1. Take the input of the number of vertex in the graph.
2. For each pair of vertex, ask user, if vertex ‘i’ is connected to vertex ‘j’.
3. If yes, then store 1 to the corresponding vertex int the incimat[] matrix.
4. Using PrintMat(), print the incidence matrix.
5. Exit.

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Runtime Test Cases
```Case 1:
Enter the number of vertexes: 3

Enter 1 if the vertex 1 is adjacent to 2, otherwise 0: 1
It is edge E(1).
Enter 1 if the vertex 1 is adjacent to 3, otherwise 0: 0

Enter 1 if the vertex 2 is adjacent to 3, otherwise 0: 1
It is edge E(2).

V(1)    V(2)    V(3)

E(1)     1     1     0

E(2)     0     1     1

Case 2:
Enter the number of vertexes: 4

Enter 1 if the vertex 1 is adjacent to 2, otherwise 0: 1
It is edge E(1).
Enter 1 if the vertex 1 is adjacent to 3, otherwise 0: 1
It is edge E(2).
Enter 1 if the vertex 1 is adjacent to 4, otherwise 0: 0

Enter 1 if the vertex 2 is adjacent to 3, otherwise 0: 1
It is edge E(3).
Enter 1 if the vertex 2 is adjacent to 4, otherwise 0: 0

Enter 1 if the vertex 3 is adjacent to 4, otherwise 0: 1
It is edge E(4).

V(1)    V(2)    V(3)    V(4)

E(1)     1     1     0     0

E(2)     1     0     1     0

E(3)     0     1     1     0

E(4)     0     0     1     1```

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