Breadth First Traversal 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.
For example, in the following graph, we start traversal from vertex 2. When we come to vertex 0, we look for all adjacent vertices of it. 2 is also an adjacent vertex of 0. If we don’t mark visited vertices, then 2 will be processed again and it will become a non-terminating process. A Breadth First Traversal of the following graph is 2, 0, 3, 1.

Following are C++ and Java implementations of simple Breadth First Traversal from a given source.

The C++ 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.

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PYTHON Programming:

# Program to print BFS traversal from a given source
# vertex. BFS(int s) traverses vertices reachable
# from s.
from collections import defaultdict
 
# This class represents a directed graph using adjacency
# list representation
class Graph:
 
    # Constructor
    def __init__(self):
 
        # default dictionary to store graph
        self.graph = defaultdict(list)
 
    # function to add an edge to graph
    def addEdge(self,u,v):
        self.graph[u].append(v)
 
    # Function to print a BFS of graph
    def BFS(self, s):
 
        # Mark all the vertices as not visited
        visited = [False]*(len(self.graph))
 
        # Create a queue for BFS
        queue = []
 
        # Mark the source node as visited and enqueue it
        queue.append(s)
        visited[s] = True
 
        while queue:
 
            # Dequeue a vertex from queue and print it
            s = queue.pop(0)
            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
            for i in self.graph[s]:
                if visited[i] == False:
                    queue.append(i)
                    visited[i] = True
 
 
# Driver code
# Create a graph given in the above diagram
g = Graph()
g.addEdge(0, 1)
g.addEdge(0, 2)
g.addEdge(1, 2)
g.addEdge(2, 0)
g.addEdge(2, 3)
g.addEdge(3, 3)
 
print "Following is Breadth First Traversal (starting from vertex 2)"
g.BFS(2)
 
# This code is contributed by Neelam Yadav

Output:

Following is Breadth First Traversal (starting from vertex 2)
2 0 3 1

Note that the above code traverses only the vertices reachable from a given source vertex. 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.

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CodingDFS and BFSGraph AlgorithmsPYTHON

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