The Graph Theorists Who Count—and What They Count

Abstract

What is a graph? To the majority of people the word “graph” conjures up a picture either of the kind of businessman’s chart shown in Figure 1, or of a smooth curve, like Figure 2, which displays the property of some mathematical function. But to a large and growing number of mathematicians this same word suggests something completely different. These are the people who are concerned, in one way or another, with the branch of mathematics known as graph theory. When they think of a graph they

have in mind a diagram consisting of a number of points, or nodes, and lines or curves joining some of these nodes to others. These lines are often called edges; an example is given in Figure 3. (Most of the other figures in this article depict graphs of one sort or another.) These objects are what the man in the street would tend to refer to as networks (a word that graph theorists use in a somewhat special sense).