# Python algorithm – Breadth First Traversal or BFS for a Graph

Python algorithm - Breadth First Traversal or BFS for a Graph - Breadth First Traversal for a graph is similar to Breadth First Traversal of a tree

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.

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
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()

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) .

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

#### Venkatesan Prabu

Wikitechy Founder, Author, International Speaker, and Job Consultant. My role as the CEO of Wikitechy, I help businesses build their next generation digital platforms and help with their product innovation and growth strategy. I'm a frequent speaker at tech conferences and events.

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