C++ Program to Find the Edge Connectivity of a Graph

In this program 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;
   list<int> *adj;
   void connections(int n, bool visited[], int disc[], int low[],
   int par[]);
   public:
      G(int n); //constructor
      void addEd(int w, int x);
      void Con();
};
G::G(int n) {
   this->n = n;
   adj = new list<int> [n];
}
//add edges to the graph
void G::addEd(int w, int x) {
   adj[x].push_back(w); //add u to v's list
   adj[w].push_back(x); //add v to u's list
}
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;
   //Go through all adjacent vertices
   list<int>::iterator i;
   for (i = adj[w].begin(); i != adj[w].end(); ++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.addEd(1, 2);
   g1.addEd(3, 2);
   g1.addEd(2, 1);
   g1.addEd(0, 1);
   g1.addEd(1, 4);
   g1.Con();
   return 0;
}

Output

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