Python Program for Breadth First Search or BFS for a Graph

22 Jun, 2022
Breadth First Traversal (or Search) for a graph is similar to Breadth First Traversal of a tree (See method 2 of this post). 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 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.
Python3
# Python3 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 representationclass 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, end = " ")             # 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 diagramg = 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
Time Complexity : O(V+E) where V is the number of vertices in graph and E is the number of edgesAuxiliary Space: O(V)Please refer complete article on Breadth First Search or BFS for a Graph for more details!
ishankhandelwals
Python Programs
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Python Program to check Armstrong Number
Python program to interchange first and last elements in a list
Differences and Applications of List, Tuple, Set and Dictionary in Python
Appending to list in Python dictionary
Python Program for simple interest
Python Program for Merge Sort
Python Program for n-th Fibonacci number
Python | Find most frequent element in a list
Python | Remove spaces from a string
Python Program to find largest element in an array