Building an undirected graph and finding shortest path using Dictionaries in Python

Last Updated : 15 Dec, 2021

Prerequisites:

In this article, we will be looking at how to build an undirected graph and then find the shortest path between two nodes/vertex of that graph easily using dictionaries in Python Language.

Building a Graph using Dictionaries

Approach: The idea is to store the adjacency list into the dictionaries, which helps to store the graph in any format not only in the form of the integers. Here we have used characters as a reference on those places any custom objects can also be used.

Below is the implementation of the above approach:

Python3

# Python3 implementation to build a  # graph using Dictionaries  from collections import defaultdict  # Function to build the graph def build_graph():     edges = [         ["A", "B"], ["A", "E"],          ["A", "C"], ["B", "D"],         ["B", "E"], ["C", "F"],         ["C", "G"], ["D", "E"]     ]     graph = defaultdict(list)          # Loop to iterate over every      # edge of the graph     for edge in edges:         a, b = edge[0], edge[1]                  # Creating the graph          # as adjacency list         graph[a].append(b)         graph[b].append(a)     return graph  if __name__ == "__main__":     graph = build_graph()          print(graph)

Output:

{    'G': ['C'],     'F': ['C'],     'E': ['A', 'B', 'D'],     'A': ['B', 'E', 'C'],     'B': ['A', 'D', 'E'],     'D': ['B', 'E'],     'C': ['A', 'F', 'G'] }

Shortest Path between two nodes of graph

Approach: The idea is to use queue and visit every adjacent node of the starting nodes that traverses the graph in Breadth-First Search manner to find the shortest path between two nodes of the graph.

Below is the implementation of the above approach:

Python3

# Python implementation to find the  # shortest path in the graph using  # dictionaries   # Function to find the shortest # path between two nodes of a graph def BFS_SP(graph, start, goal):     explored = []          # Queue for traversing the      # graph in the BFS     queue = [[start]]          # If the desired node is      # reached     if start == goal:         print("Same Node")         return          # Loop to traverse the graph      # with the help of the queue     while queue:         path = queue.pop(0)         node = path[-1]                  # Condition to check if the         # current node is not visited         if node not in explored:             neighbours = graph[node]                          # Loop to iterate over the              # neighbours of the node             for neighbour in neighbours:                 new_path = list(path)                 new_path.append(neighbour)                 queue.append(new_path)                                  # Condition to check if the                  # neighbour node is the goal                 if neighbour == goal:                     print("Shortest path = ", *new_path)                     return             explored.append(node)      # Condition when the nodes      # are not connected     print("So sorry, but a connecting"\                 "path doesn't exist :(")     return  # Driver Code if __name__ == "__main__":          # Graph using dictionaries     graph = {'A': ['B', 'E', 'C'],             'B': ['A', 'D', 'E'],             'C': ['A', 'F', 'G'],             'D': ['B', 'E'],             'E': ['A', 'B', 'D'],             'F': ['C'],             'G': ['C']}          # Function Call     BFS_SP(graph, 'A', 'D')

Output:

Shortest path =  A B D

Building an undirected graph and finding shortest path using Dictionaries in Python

murtuza_chawala

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Building an undirected graph and finding shortest path using Dictionaries in Python

Building a Graph using Dictionaries

Shortest Path between two nodes of graph

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