Breadth First Search Traversal in a Graph

Breadth First Traversal (or Search) for a graph is similar to Breadth First Traversal of a tree. The only catch here is, unlike trees, graphs may contain cycles, so we may come to the same node again.To avoid processing a node more than once, we use a boolean visited array.

For simplicity, it is assumed that all vertices are reachable from the starting vertex (source vertex, in this case 2).

For example, in the following graph, we start the traversal from Vertex-2. When we come to Vertex-0, we look for all adjacent vertices of Vertex-0. Vertex-2 is also an adjacent of Vertex-0. If we don’t mark visited vertices, then Vertex-2 will get processed again and it will become a non-terminating process.

A Breadth First Traversal of the following graph should be 2, 0, 1, 4, 3.

Following are the implementations of simple Breadth First Traversal from a given source.

The implementation uses adjacency list representation of graphs. STL‘s list container is used to store lists of adjacent nodes and queue of nodes needed for BFS traversal.

class Graph 
{ 
   private int V; // No. of vertices 
   private LinkedList adj[]; //Adjacency Lists 

   // Constructor 
   Graph(int v) 
   { 
      V = v; 
      adj = new LinkedList[v]; 
      for (int i=0; i queue = new LinkedList(); 

      // Mark the current node as visited and enqueue it 
      visited[s]=true; 
      queue.add(s); 

      while (queue.size() != 0) 
      { 
         // Dequeue a vertex from queue and print it 
         s = queue.poll(); 
         System.out.print(s+" "); 

         // Get all adjacent vertices of the dequeued vertex s 
         // If a adjacent has not been visited, then mark it 
         // visited and enqueue it 
         Iterator i = adj[s].listIterator(); 
         while (i.hasNext()) 
         { 
            int n = i.next(); 
            if (!visited[n]) 
            { 
               visited[n] = true; 
               queue.add(n); 
            } 
         } 
      } 
   } 

   // Driver method to 
   public static void main(String args[]) 
   { 
      Graph g = new Graph(4); 

      g.addEdge(0, 1); 
      g.addEdge(0, 2); 
      g.addEdge(1, 2); 
      g.addEdge(2, 0); 
      g.addEdge(2, 3); 
      g.addEdge(3, 3); 

      System.out.println("Following is Breadth First Traversal "+ 
                  "(starting from vertex 2)"); 

      g.BFS(2); 
   } 
} 

Put image

All the vertices may not be reachable from a given vertex (example Disconnected graph). To print all the vertices, we can modify the BFS function to do traversal starting from all nodes one by one (Like the DFS modified version) .

Time Complexity: O(V+E) where V is number of vertices in the graph and E is number of edges in the graph