How does breadth-first search (BFS) traverse a graph?

Breadth-first search (BFS) is a systematic method for traversing or searching through a graph. The fundamental characteristic of BFS is that it explores all neighbors of a node before moving on to the next level of neighbors. This means that when BFS starts at a source node, it first visits all nodes that are directly connected to the source (i.e., its immediate neighbors). Once all these nodes are explored, BFS proceeds to explore the next level of nodes, which are the neighbors of the previously visited nodes.

This level-order exploration continues until all reachable nodes have been visited. The result of this process is that BFS effectively covers layers of the graph in a breadth-first manner, ensuring that all nodes at a particular depth are processed before moving deeper into the graph. This is particularly useful for finding the shortest path in unweighted graphs since BFS will always find the shortest distance from the starting node to all other nodes by virtue of its level-order traversal.