# C++ Program to Find the Maximum Cut in a Graph

In this program to find the maximum Cut in a graph, we need to find the Edge Connectivity of a Graph. An Edge Connectivity of a Graph of a graph means it is a bridge, removing it graph will be disconnected. Number of connected components increases with the removing of bridge in a disconnected undirected graph.

## Functions and pseudocode

Begin
Function connections() is a recursive function to find out the connections:
A) Mark the current node un visited.
B) Initialize time and low value
C) Go through all vertices adjacent to this
D) Check if the subtree rooted with x has a connection to one
of the ancestors of w. If the lowest vertex reachable from
subtree under x is below u in DFS tree, then w-x has a
connection.
E) Update low value of w for parent function calls.
End
Begin
Function Con() that uses connections():
A) Mark all the vertices as unvisited.
B) Initialize par and visited, and connections.
C) Print the connections between the edges in the graph.
End

## Example

#include<iostream>
#include <list>
#define N -1
using namespace std;
class G {
//declaration of functions
int n;
void connections(int n, bool visited[], int disc[], int low[], int par[]);
public:
G(int n); //constructor
void Con();
};
G::G(int n) {
this->n= n;
}
void G::addEd(int w, int x) {
}
void G::connections(int w, bool visited[], int dis[], int low[],
int par[]) {
static int t = 0;
//mark current node as visited
visited[w] = true;
dis[w] = low[w] = ++t;
list<int>::iterator i;
int x = *i; //x is current adjacent
if (!visited[x]) {
par[x] = w;
connections(x, visited, dis, low, par);
low[w] = min(low[w], low[x]);
// If the lowest vertex reachable from subtree under x is below w in DFS tree, then w-x is a connection
if (low[x] > dis[w])
cout << w << " " << x << endl;
}
else if (x != par[w])
low[w] = min(low[w], dis[x]);
}
}
void G::Con() {
// Mark all the vertices as unvisited
bool *visited = new bool[n];
int *dis = new int[n];
int *low = new int[n];
int *par = new int[n];
for (int i = 0; i < n; i++) {
par[i] = N;
visited[i] = false;
}
//call the function connections() to find edge connections
for (int i = 0; i < n; i++)
if (visited[i] == false)
connections(i, visited, dis, low, par);
}
int main() {
cout << "\nConnections in first graph \n";
G g1(5);
g1.Con();
return 0;
}

## Output

Connections in first graph
2 3
1 2
1 4
0 1