As graphs are a very important data structure, it is important for us to have good algorithms that work with them as well. Graph algorithms play an vital role in the solutions of many problems in computer science, and also in engineering problems such as analyses of traffic congestion and optimization of flow over pipeline networks carrying fluids. Even where the problem domain itself does not use graphs, it is sometimes seen that the problem can be transformed into an equivalent one over graphs, so that the solution of the equivalent problem would literally translate into a solution of the original problem as well.

One of the simplest graph algorithms, and a model or a component of many other graph algorithms as well, is "breadth-first search." The basic notion is to start with a distinguished node in the graph which is called the source or the...