C++ Program to Check the Connectivity of Undirected Graph Using DFS

To check connectivity of a graph, we will try to traverse all nodes using any traversal algorithm. After completing the traversal, if there is any node, which is not visited, then the graph is not connected.

For the undirected graph, we will select one node and traverse from it.

In this case the traversal algorithm is recursive DFS traversal.

Input − Adjacency matrix of a graph

Output − The Graph is connected.

Algorithm

traverse(u, visited)

Input − The start node u and the visited node to mark which node is visited.

Output: Traverse all connected vertices.

Begin
   mark u as visited
   for all vertex v, if it is adjacent with u, do
      if v is not visited, then
         traverse(v, visited)
   done
End

isConnected(graph)

Input − The graph.

Output − True if the graph is connected.

Begin
   define visited array
      for all vertices u in the graph, do
         make all nodes unvisited
         traverse(u, visited)
         if any unvisited node is still remaining, then
            return false
      done
   return true
End

Example Code

 Live Demo

#include<iostream>
#define NODE 5
using namespace std;
int graph[NODE][NODE] = {{0, 1, 1, 0, 0},
{1, 0, 1, 1, 0},
{1, 1, 0, 1, 1},
{0, 1, 1, 0, 1},
{0, 0, 1, 1, 0}};
void traverse(int u, bool visited[]) {
   visited[u] = true; //mark v as visited
   for(int v = 0; v<NODE; v++) {
      if(graph[u][v]) {
         if(!visited[v])
            traverse(v, visited);
      }
   }
}
bool isConnected() {
   bool *vis = new bool[NODE];
   //for all vertex u as start point, check whether all nodes are visible or not
   for(int u; u < NODE; u++) {
      for(int i = 0; i<NODE; i++)
         vis[i] = false; //initialize as no node is visited
         traverse(u, vis);
      for(int i = 0; i<NODE; i++) {
         if(!vis[i]) //if there is a node, not visited by traversal, graph is not connected
            return false;
      }
   }
   return true;
}
int main() {
   if(isConnected())
      cout << "The Graph is connected.";
   else
      cout << "The Graph is not connected.";
}

Output:

The Graph is connected.