Given a graph G = (V, E) and a source vertex s, breadth-first search explores the edges of G systematically to discover every vertex that is reachable from s. While doing so, it computes the smallest number of edges from s to each reachable vertex, making it suitable to solve the single-source shortest path problem on unweighted graphs, or graphs whose edges all have the same weight.
Breadth-First Search (BFS) is named so because it expands the frontier between discovered and undiscovered vertices uniformly across the breadth of the frontier. In that sense, the algorithm first explores vertices at distance k from s before discovering vertices at distance k + 1. To keep track of progress, breadth-first search identifies ...
