Networks are objects that contain nodesand edges between pairs of nodes. They can be used to represent a wide variety of real-world situations, such as distribution and scheduling. Mathematically, networks are useful for visualizing combinatorial problems and make for a rich and fascinating theory.

There are, of course, several different kinds of networks. We will mostly deal with simple networks, where edges connect two distinct nodes (so there are no self-loops), there is, at most, one edge between any two nodes, and all the edges are bidirectional. A treeis a special kind of network in which there are no cycles; that is, there are no lists of nodes in which each node is connected to the following node by an edge, and the final node is connected to the first. Trees are especially simple in terms of their theory because they connect a number of nodes with the fewest possible edges. A complete...