# Graph Representation using Incidence List in C++

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

Problem Description

1. This algorithm represent a graph using incidence list.
2. The time complexity of this algorithm is O(e).

Problem Solution

1. This algorithm takes the input of the number of vertex and edges.
2. Then it takes the input of connected vertex pairs.
3. Print the incidence list.
4. Exit.

Program/Source Code

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

```#include<iostream>

using namespace std;

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

// take the input of the number of edges.
cout<<"Enter the number of vertexes of the graph: ";
cin>>v;
cout<<"\nEnter the number of edges of the graph: ";
cin>>e;
int edge[e][2];

// Take the input of the adjacent vertex pairs of the given graph.
for(i = 0; i < e; i++)
{
cout<<"\nEnter the vertex pair for edge "<<i+1;
cout<<"\nV(1): ";
cin>>edge[i][0];
cout<<"V(2): ";
cin>>edge[i][1];
}

// Print the incidence list representation of the graph.
cout<<"\n\nThe incidence list representation for the given graph: ";
for(i = 0; i < e; i++)
{
// For each vertex print, its adjacent vertex.
cout<<"\n\tE("<<i+1<<") -> { ";
cout<<"V("<<edge[i][0]<<") , "<<"V("<<edge[i][1]<<")";
cout<<" }";
}
}```
Program Explanation

1. Take the input of the number of vertex ‘v’ and edges ‘e’.
2. Take the input of ‘e’ pairs of vertexes of the given graph in edge[][].
3. Now for each edge print the corresponding vertex involved in that connection.
4. Exit.

Runtime Test Cases
```Case 1:
Enter the number of vertexes of the graph: 5

Enter the number of edges of the graph: 8

Enter the vertex pair for edge 1
V(1): 1
V(2): 3

Enter the vertex pair for edge 2
V(1):1
V(2): 4

Enter the vertex pair for edge 3
V(1): 1
V(2): 5

Enter the vertex pair for edge 4
V(1): 2
V(2): 3

Enter the vertex pair for edge 5
V(1): 2
V(2): 5

Enter the vertex pair for edge 6
V(1): 3
V(2): 4

Enter the vertex pair for edge 7
V(1): 3
V(2): 5

Enter the vertex pair for edge 8
V(1): 4
V(2): 5

The incidence list representation for the given graph:
E(1) -> { V(1) , V(3) }
E(2) -> { V(1) , V(4) }
E(3) -> { V(1) , V(5) }
E(4) -> { V(2) , V(3) }
E(5) -> { V(2) , V(5) }
E(6) -> { V(3) , V(4) }
E(7) -> { V(3) , V(5) }
E(8) -> { V(4) , V(5) }
Case 2:
Enter the number of vertexes of the graph: 3

Enter the number of edges of the graph: 2

Enter the vertex pair for edge 1
V(1): 1
V(2): 3

Enter the vertex pair for edge 2
V(1): 2
V(2): 3

The incidence list representation for the given graph:
E(1) -> { V(1) , V(3) }
E(2) -> { V(2) , V(3) }```

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