The co-authorship network of scientists represents a prototype of complex evolving networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an eight-year period (1991-98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network's time evolution. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically.Comment: 14 pages, 15 figure

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We suggest that a h-type index -equal to h if you have published h papers, each of which has at least h citations -would be a useful supplement to journal impact factors.Recently, Hirsch 2 proposed what he called the "h-index" (a scientist has index h if h of his/her N papers have at least h citations each, and the other (N−h) papers have fewer than h citations each) to quantify an individual's scientific output. The idea was effectively publicized by Ball's news item in Nature, 3 and it has got positive reception in the physics community 4,5 and also in the scientometrics literature. 6 Yet, its widespread use will presumably be severely hindered by a series of technical shortcomings (e. g., the lack of common consent on disciplinary and sub-disciplinary standards, on the proper weighting of co-authorship, etc.) and, most of all, by the natural and justifiable resistance of the scientific community to use however igenious numerical indices to assess individual research performances. * An extended version of a paper published in The Scientist. 1

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