Traversing a Graph

A common activity on a graph is visiting each vertex of it in a given order. We will start by introducing the breadth-first search, and then follow with depth-first search. Both of these techniques form the archetype for many important graph algorithms, as we will see later with the cycle detection and Dijkstra's algorithm for single-source shortest paths.

Breadth-First Search

Given a graphG = (V, E)and a source vertexs, breadth-first search explores the edges ofGsystematically to discover every vertex that is reachable froms. While doing so, it computes the smallest number of edges fromsto 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 distancekfrom...