When traversing a graph using BFS, what is the systematic approach taken?

When traversing a graph using Breadth-First Search (BFS), the systematic approach involves exploring nodes in layers from the starting vertex. This means that BFS aims to visit all the neighbors of a given node before moving onto the neighbors of the neighbors.

The traversal starts at a specific initial node and explores all its direct connections. Once all these nodes have been visited, BFS then advances to the next layer, which includes all the nodes that are directly connected to the nodes from the previous layer. This layering continues until all reachable nodes have been visited.

This method ensures that the shortest path (in terms of edge count) to each node is found, as BFS effectively explores all nodes at the present "depth" before moving onto nodes at the next depth level. It is particularly useful in scenarios where the goal is to find the minimum distance between nodes or to explore all possibilities level-by-level.