A directed graph is said to be strongly connected when it is possible to visit every node of the graph from any node. Here we are discussing simple approach to check if a directed graph is strongly connected nor not.

Prerequisite:- BFS algorithm must be known to check is the directed graph is strongly connected or not. If you don't know BFS (Breadth First Search) algorithm or implementation click the link given below.

See also: Implementation of BFS Algorithm

traversal then go to step 2 otherwise reuturn false.

of all edges).

visited during the traversal then return true otherwise return false.

The above graph is strongly connected because it is possible to visite every node from any vertex of the graph.

The above graph is not strongly connected as you can see we can't visit any single node from vertex 2.

Prerequisite:- BFS algorithm must be known to check is the directed graph is strongly connected or not. If you don't know BFS (Breadth First Search) algorithm or implementation click the link given below.

See also: Implementation of BFS Algorithm

**Algorithm to check if a Directed Graph is Strongly Connected or Not****step 1:**Do the BFS traversal of the graph from any vertex

**v,**if every node is visited during the

traversal then go to step 2 otherwise reuturn false.

**step 2:**Transpose the graph (i.e Don't disturb the arrangement of vertices, but reverse the direction

of all edges).

**step 3:**Mark all the Nodes unvisited again.

**step 4:**Do the BFS traversal of the transposed graph again from the same vertex

**v,**if every vertex is

visited during the traversal then return true otherwise return false.

**Examples:**The above graph is strongly connected because it is possible to visite every node from any vertex of the graph.

The above graph is not strongly connected as you can see we can't visit any single node from vertex 2.

**Both the example are check through the program given below. Outputs for the both above examples are given below.****C++ Program is given below to check if the given directed graph is strongly connected or Not.**#include <stdio.h> #include <queue> #define MAX 100 #define visited 2 #define unvisited 1 using namespace std; class bfs_traversal { public: std::queue <int> que; int vertex_status[MAX],graph_matrix[MAX][MAX]; int n,vertex_count; public: void get_data(); bool bfs_traverse(); void transpose(); }; void bfs_traversal::get_data() { printf("\nEnter the total number of vertices: "); scanf("%d",&n); int max_edge=n*(n-1); int i,source,destination; for(i=1;i<=max_edge;i++) { printf("\nEnter the source and destination of edge %d and (0,0) to Exit:\n",i); scanf("%d%d",&source,&destination); if(source==0 && destination==0) { break; } else { graph_matrix[source][destination]=1; } } } bool bfs_traversal::bfs_traverse() { /* marking all vertex unvisited */ int i; for(i=1;i<=n;i++) { vertex_status[i]=unvisited; } /* starting bfs traversal from the source */ int source; printf("\nEnter the source to start bfs: \n"); scanf("%d",&source); printf("\nThe bfs traversal is: \n"); printf("\n%d ",source); vertex_status[source]=visited; vertex_count=1; que.push(source); while(!que.empty()) { source=que.front(); que.pop(); for(i=1;i<=n;i++) { if(graph_matrix[source][i]==1 && vertex_status[i]==unvisited) { printf("%d ",i); vertex_status[i]=visited; que.push(i); vertex_count++; } } } /* Checking if every node is visited during bfs traversal */ if(vertex_count==n) { return true; } else { return false; } } void bfs_traversal::transpose() { int temp; for(int i=1;i<=n;i++) { for(int j=i;j<=n;j++) { temp=graph_matrix[i][j]; graph_matrix[i][j]=graph_matrix[j][i]; graph_matrix[j][i]=temp; } } } int main() { bfs_traversal graph; graph.get_data(); if(graph.bfs_traverse()) { graph.transpose(); if(graph.bfs_traverse()) { printf("\nGraph is Strongly Connected"); } else { printf("\nGraph is not Strongly Connected"); } } else { printf("\nGraph is not Strongly Connected"); } return 0; }

**OUTPUT OF THE EXAMPLE 1:****OUTPUT OF THE EXAMPLE 2:**
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