# Graph Representation using Adjacency Matrix in C++

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

Problem Description

1. This algorithm represents a graph using adjacency matrix.
2. This method of representing graphs is not efficient.
3. 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.
4. Exit.

Program/Source Code

C++ program to represent graph using adjacency 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 adjacency matrix.
void PrintMat(int mat[], int n)
{
int i, j;

cout<<"\n\n"<<setw(4)<<"";
for(i = 0; i < n; i++)
cout<<setw(3)<<"("<<i+1<<")";
cout<<"\n\n";

// Print 1 if the corresponding vertexes are connected otherwise 0.
for(i = 0; i < n; i++)
{
cout<<setw(3)<<"("<<i+1<<")";
for(j = 0; j < n; j++)
{
cout<<setw(4)<<mat[i][j];
}
cout<<"\n\n";
}
}

int main()
{
int i, j, v;

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

int  mat;

cout<<"\n";
// Take input of the adjacency of each pair of vertexes.
for(i = 0; i < v; i++)
{
for(j = i; j < v; j++)
{
if(i != j)
{
cout<<"Enter 1 if the vertex "<<i+1<<" is adjacent to "<<j+1<<", otherwise 0: ";
cin>>mat[i][j];

mat[j][i] = mat[i][j];
}
else
mat[i][j] = 0;
}
}

PrintMat(mat, v);
}```
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 in the matrix.
4. Using PrintMat(), print the adjacency matrix.
5. Exit.

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Runtime Test Cases
```Case 1:
Enter the number of vertexes: 4

Enter 1 if the vertex 1 is adjacent to 2, otherwise 0: 1
Enter 1 if the vertex 1 is adjacent to 3, otherwise 0: 0
Enter 1 if the vertex 1 is adjacent to 4, otherwise 0: 1
Enter 1 if the vertex 2 is adjacent to 3, otherwise 0: 0
Enter 1 if the vertex 2 is adjacent to 4, otherwise 0: 1
Enter 1 if the vertex 3 is adjacent to 4, otherwise 0: 0

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

(1)   0   1   0   1

(2)   1   0   0   1

(3)   0   0   0   0

(4)   1   1   0   0

Case 2:
Enter the number of vertexes: 3

Enter 1 if the vertex 1 is adjacent to 2, otherwise 0: 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

(1)  (2)  (3)

(1)   0   1   0

(2)   1   0   1

(3)   0   1   0```

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