Implementing two Graph traversal algorithms in Python: Depth First Search and Breadth First Search

Posted on Sa 24 Januar 2015 in Learning

Depth First Search and Breadth First Search

I am right in front of a ton of exams and I need to learn about algorithms and data structures. When I read about pseudocode of Graph traversal algorithms, I thought:
Why not actually implement them in a real programming language? So I did so and now you can study my code now here. I guess this problem was solved a thousand times before, but I learnt something and I hope my approach has some uniqueness to it.

Additionlay, you can also generate a topological order after you traversed the whole Graph, which is a nice little extra.

If you want the most recent version of the code, you can visit its own Github repo here.

Well, here's the code. Just download and run it like this: python

# -*- coding: utf-8 -*-

__author__ = 'Nikolai Tschacher'
__version__ = '0.1'
__contact__ = ''

import time
from collections import deque

This is just a little representation of two basic graph traversal methods.

    - Depth-First-Search
    - Breadth-First-Search

It's by no means meant to be fast or performant. Rather it is for educational
purposes and to understand it better for myself.

class Node(object):
    """Represents a node."""

    def __init__(self, name): = name
        self._visited = 0
        self.discovery_time = None
        self.finishing_time = None

    def neighbors(self, adjacency_list):
        return adjacency_list[self]

    def visited(self):
        return self._visited

    def visited(self, value):
        if value == 1:
            self.discovery_time = time.clock()
        elif value == 2:
            self.finishing_time = time.clock()

        self._visited = value

    def __str__(self):
        return str(

    def __repr__(self):
        return str(

# Let's define our sample graph and represent it in an adjacency list.
# This means that for every node, we store the outgoing edges in a list.

Nodes = [Node(i) for i in range(10)]

Graph = {
    Nodes[0]: [Nodes[5], Nodes[3]],
    Nodes[1]: [Nodes[8], Nodes[3]],
    Nodes[2]: [Nodes[5]],
    Nodes[3]: [Nodes[9], Nodes[8]],
    Nodes[4]: [Nodes[5], Nodes[2]],
    Nodes[5]: [Nodes[9]],
    Nodes[6]: [Nodes[9]],
    Nodes[7]: [Nodes[5], Nodes[2], Nodes[6]],
    Nodes[8]: [Nodes[9], Nodes[4]],
    Nodes[9]: [Nodes[0], Nodes[1]],


Running time: O(|V| + |E|)

def depth_first_search(Graph, Nodes):
    for node in Nodes:
        node.visited = 0

    for node in Nodes:
        if node.visited == 0:
            depth_first_search_visit(Graph, node)

def depth_first_search_visit(Graph, node):
    node.visited = 1
    for neighbor in node.neighbors(Graph):
        if neighbor.visited == 0:
            depth_first_search_visit(Graph, neighbor)
    node.visited = 2


def breadth_first_search(Graph, Nodes):
    for node in Nodes:
        node.visited = 0

    for node in Nodes:
        if node.visited == 0:
            breadth_first_search_visit(Graph, node)

def breadth_first_search_visit(Graph, node):
    node.visited = 1
    queue = deque([node])

    while True:
            u = queue.popleft()
        except IndexError:

        for neighbor in u.neighbors(Graph):
            if neighbor.visited == 0:
                neighbor.visited = 1
        node.visited = 2

def print_topological(Nodes):
    print('Toplogical sort of the Graph:')
    # prints a topological sort
    for node in sorted(Nodes, key=lambda obj: obj.finishing_time):
        print('\t {}: {}'.format(node, node.finishing_time))

if __name__ == '__main__':
    print('Using Depth-First-Search')
    # should print each node exactly once
    depth_first_search(Graph, Nodes)


    # the same buth with Breadth-First-Search
    print('Using Breadth-First-Search')
    breadth_first_search(Graph, Nodes)