BFS works best when there is a concept of layers or levels of neighborhoods in the aGraph we are dealing with. For example, when the connections of a person in LinkedIn are expressed as a graph, there are first-level connections and then there are second-level connections, which directly translate to the layers.

The BFS algorithm starts from a root vertex and explores the vertices in the neighborhood vertices. It then moves to the next neighborhood level and repeats the process.

Let's look at a BFS algorithm. For that, let's first consider the following undirected graph: 

Let's start by calculating the immediate neighborhood of each vertex and store that in a list, called an adjacency list. In Python, we can use the dictionary data structure to store it:

graph={ 'Amin'   : {'Wasim', 'Nick', 'Mike'},
         'Wasim' : {'Imran', 'Amin'}, 
         'Imran' : {'Wasim','Faras'}, 
         'Faras' : {'Imran'},
         'Mike'  : {'Amin'}, 
         'Nick' :  {'Amin'}}

To implement it in Python, we proceed as follows.

We will first explain the initialization and then the main loop.