  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.
