## The World Wide Web A Graph

Consider the World Wide Web as a graph. The Web's architecture as is a hemocoel's is non-engineered. The edges are a virtual network of hyperlinks, connecting more than eight billion web pages. These pages, created by tens of millions of independent people at separate locations are the vertices. Large computers can scarcely contain these data points, but after cataloging what we know of each vertex and edge, we can create a model simplifying the WWW but retaining some properties of its larger graph.

From smaller representative data sets we better appreciate global and local relationships, and later we apply these to the larger graph. For example, growth at vertices both in the web and in hemocoels, is decentralized but self-organized. The web contains a large, strongly connected core of prominent sites through which every page can reach every other page over a shortest path of sixteen to twenty hyperlinks. Distances through this core are much shorter than across the whole web. Local actions grow new vertices near the old ones, and the chance that an existing vertex or link receives a new link is proportional to the number of links the vertex already has, resulting in a power law distribution of links (Ref: Power Laws).

But growth patterns differ: Classical random graphs are regular graphs (almost all their vertices have the same expected number of edges), but in real-world graphs a few vertices have very large numbers of edges. We can extend our random graph model to include these new forms (Ref: Algorithm Design).

Understanding local behavior at neighboring vertices of the WWW lets us reason that an unusually large number of links among a small set of vertices, or web pages suggests these pages may be related to the same topic and that the group may even be a signature for the area. For example, in the hemocoel, the edges leading to vertices at or near the openings of the Malpighian tubules might suggest excretory metabolites and processes, so computing these network flows might partition the hemocoel into regional functional graphs. To build is to understand.

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