Chapters 10 through 12 explained trees. This chapter describes a related data structure: the network. Like a tree, a network contains nodes that are connected by links. Unlike the nodes in a tree, the nodes in a network don't necessarily have a hierarchical relationship. In particular, the links in a network may create cycles, so a path that follows the links could loop back to its starting position.

This chapter explains networks and some basic network algorithms, such as detecting cycles, finding shortest paths, and finding a tree that is part of the network that includes every node.

Network terminology isn't quite as complicated as tree terminology, because it doesn't borrow as many terms from genealogy, but it's still worth taking a few minutes to review the relevant terms.

A network consists of a set of *nodes* connected by *links*. (Sometimes, particularly when you're working on mathematical algorithms and theorems, a network is called a *graph*, nodes are called *vertices*, and links are called *edges*.) If node A and node B are directly connected by a link, they are *adjacent* and are called *neighbors*.

Unlike the case with a tree, a network has no root node, although there may be particular nodes of interest, depending on the network. For example, a transportation network might contain special hub nodes where buses, trains, ferries, or other vehicles start and end their routes.

A link can be *undirected* (you can traverse it in ...

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