The study of networks has become one of the great scientific hotbeds of this new century, though mathematicians and others have been studying networks for many hundreds of years. Recent developments in computer technology (i.e., the Internet), and in social theory (the social network, popularly conceived in the concept of “six degrees of separation”), have put a spotlight on the study of networks.

In this chapter, we look at how networks are modeled with graphs. We're not talking about the graphs such as pie graphs or bar graphs. We define what a graph is, how they're represented in VB.NET, and how to implement important graph algorithms. We also discuss the importance of picking the correct data representation when working with graphs, since the efficiency of graph algorithms is dependent on the data structure used.

GRAPH DEFINITIONS

A graph consists of a set of vertices and a set of edges. Think of a map of your state. Each town is connected with other towns via some type of road. A map is a type of graph. Each town is a vertex and a road that connects two towns is an edge. Edges are specified as a pair, (v1, v2), where v1 and v2 are two vertices in the graph. A vertex can also have a weight, sometimes also called a cost.