  Many complex systems, including networks, are not static but can display
strong fluctuations at various time scales. Characterizing the dynamics in
complex networks is thus of the utmost importance in the understanding of these
networks and of the dynamical processes taking place on them. In this article,
we study the example of the US airport network in the time period 1990-2000. We
show that even if the statistical distributions of most indicators are
stationary, an intense activity takes place at the local (`microscopic') level,
with many disappearing/appearing connections (links) between airports. We find
that connections have a very broad distribution of lifetimes, and we introduce
a set of metrics to characterize the links' dynamics. We observe in particular
that the links which disappear have essentially the same properties as the ones
which appear, and that links which connect airports with very different traffic
are very volatile. Motivated by this empirical study, we propose a model of
dynamical networks, inspired from previous studies on firm growth, which
reproduces most of the empirical observations both for the stationary
statistical distributions and for the dynamical properties.
