Before we delve into implementing Dijkstra’s Algorithm, we need a graph to explore it, but how exactly do we represent graphs in python? One of the ways to represent graph is through an adjacency list using a Python dictionary.

Take a look at the following graph represented by an adjacency list:

graph = {
  'A': [('B', 10), ('C', 3)],
  'B': [('C', 3), ('D', 2)],
  'C': [('D', 2)],
  'D': [('E', 10)],
  'E': [('B', 15)],
}

Reading this adjacency list, we can tell the graph has 5 vertices: 'A', 'B', 'C', 'D', 'E'.

There is a path from 'A' to 'B' with a cost (or edge weight) of 10 and a path from 'A' to 'C' with a cost of 3.

There is a path from 'B' to 'C' with a cost of 3 and a path from 'B' to 'D' with a cost of 2.

There is a path from 'C' to 'D' with a cost of 2.

There is a path from 'D' to 'E' with a cost of 10.

There is a path from 'E' to 'B' with a cost of 15.