Part I of this article, in the January-February issue, discussed
some very large structures that can usefully be looked upon as
mathematical graphs. In this context a graph is a set of
vertices (which are usually represented as dots) and a set of
edges (lines between the dots). One large object that can be
described in this way is the World Wide Web; its 800 million
pages are the vertices of a graph, and links from one page to
another are the edges. A second example comes out of Hollywood:
The vertices are 225,000 actors, and an edge connects any two
actors who have appeared in a feature film together. Although
graph theory has a history of two centuries and more, only in
recent years has it been applied routinely to structures like
these, with many thousands or millions of vertices and edges.
Studying such enormous graphs is by no means easy. The Hollywood
collaboration graph just barely fits in the memory of a large
computer. The Web, a few orders of magnitude larger, requires
all the resources of the Inter