Check if a directed graph is connected or not in C++

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 directed graph, we will start traversing from all nodes to check connectivity. Sometimes one edge can have only outward edge but no inward edge, so that node will be unvisited from any other starting node.

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

 Live Demo

#include<iostream> #define NODE 5 using namespace std; int graph[NODE][NODE] = {{0, 1, 0, 0, 0},    {0, 0, 1, 0, 0},    {0, 0, 0, 1, 1},    {1, 0, 0, 0, 0},    {0, 1, 0, 0, 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.