The pages and hyperlinks of the World-Wide Web maybe viewed as nodes and edges in a directed graph. This graph has about a billion nodes today,several billion links, and appears to grow exponentially with time. There are many reasons---mathematical, sociological, and commercial---for studying the evolution of this graph. We first review a set of algorithms that operate on the Web graph, addressing problems from Web search, automatic community discovery, and classification. We then recall a number of measurements and properties of the Web graph. Noting that traditional random graph models do not explain these observations, we propose a new family of random graph models.

The contemporary structure of scientific activity, including the publication of papers in academic journals, citation behaviour, the clustering of research into specialties and so on has been intensively studied over the last fifty years. A number of quantitative relationships between aspects of the system have been observed. This paper reports on a simulation designed to see whether it is possible to reproduce the form of these observed relationships using a small number of simple assumptions. The simulation succeeds in generating a specialty structure with 'areas' of science displaying growth and decline. It also reproduces Lotka's Law concerning the distribution of citations among authors. The simulation suggests that it is possible to generate many of the quantitative features of the present structure of science and that one way of looking at scientific activity is as a system in which scientific papers generate further papers, with authors (scientists) playing a necessary but incidental role. The theoretical implications of these suggestions are briefly explored.

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