Check if a Directed Graph is Strongly Connected in C++

Suppose we have a graph. We have to check whether the graph is strongly connected or not. A graph is said to be strongly connected, if any two vertices have a path between them, then the graph is connected. An undirected graph is strongly connected graph. Some undirected graph may be connected but not strongly connected. This is an example of a strongly connected graph.

This is an example of a connected, but not strongly connected graph.

Here we will see, how to check a graph is strongly connected or not using the following steps.

Steps −

• Mark all nodes as not visited

• Start DFS traversal from any arbitrary vertex u. If the DFS fails to visit all nodes, then return false.

• Reverse all edges of the graph

• Set all vertices as not visited nodes again

• Start DFS traversal from that vertex u. If the DFS fails to visit all nodes, then return false. otherwise true.

Example

 Live Demo

#include <iostream>
#include <list>
#include <stack>
using namespace std;
class Graph {
   int V;
   list<int> *adj;
   void dfs(int v, bool visited[]);
   public:
   Graph(int V) {
      this->V = V;
      adj = new list<int>[V];
   }
   ~Graph() {
      delete [] adj;
   }
   void addEdge(int v, int w);
   bool isStronglyConnected();
   Graph reverseArc();
};
void Graph::dfs(int v, bool visited[]) {
   visited[v] = true;
   list<int>::iterator i;
   for (i = adj[v].begin(); i != adj[v].end(); ++i)
   if (!visited[*i])
   dfs(*i, visited);
}
Graph Graph::reverseArc() {
   Graph graph(V);
   for (int v = 0; v < V; v++) {
      list<int>::iterator i;
      for(i = adj[v].begin(); i != adj[v].end(); ++i)
         graph.adj[*i].push_back(v);
   }
   return graph;
}
void Graph::addEdge(int u, int v) {
   adj[u].push_back(v);
}
bool Graph::isStronglyConnected() {
   bool visited[V];
   for (int i = 0; i < V; i++)
   visited[i] = false;
   dfs(0, visited);
   for (int i = 0; i < V; i++)
      if (visited[i] == false)
         return false;
   Graph graph = reverseArc();
   for(int i = 0; i < V; i++)
      visited[i] = false;
   graph.dfs(0, visited);
   for (int i = 0; i < V; i++)
      if (visited[i] == false)
         return false;
   return true;
}
int main() {
   Graph graph(5);
   graph.addEdge(0, 1);
   graph.addEdge(1, 2);
   graph.addEdge(2, 3);
   graph.addEdge(3, 0);
   graph.addEdge(2, 4);
   graph.addEdge(4, 2);
   graph.isStronglyConnected()? cout << "This is strongly connected" : cout << "This is not strongly connected";
}

Output

This is strongly connected