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

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 Dictonaries

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



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# Python3 implementation to build a 
# graph using Dictonaries
  
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)

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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 is traverse 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

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# 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]
          
        # Codition 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')

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Output:

Shortest path =  A B D

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