Exploring graph algorithms

Graph algorithms are critical in solving problems related to graphs, such as finding the shortest path between two nodes or detecting cycles. This section will discuss two graph traversal algorithms: BFS and DFS.

Breadth-first search

BFS is a graph traversal algorithm that starts at the root node and explores all the neighboring nodes at a particular level before moving to the next level of nodes. It works by maintaining a queue of nodes to visit and marking each visited node as it is added to the queue. The algorithm then dequeues the next node in the queue and explores all its neighbors, adding them to the queue if they haven’t been visited yet.

The behavior of a BFS is illustrated in Figure 2.7:

Figure 2.7 – Example of graph traversal made by a breadth-first search

Let’s now see how we can implement it in Python:

1. We create an empty graph and add edges with the add_edges_from() method:

   G...