  Many natural and artificial networks evolve in time. Nodes and connections
appear and disappear at various timescales, and their dynamics has profound
consequences for any processes in which they are involved. The first empirical
analysis of the temporal patterns characterizing dynamic networks are still
recent, so that many questions remain open. Here, we study how random walks, as
paradigm of dynamical processes, unfold on temporally evolving networks. To
this aim, we use empirical dynamical networks of contacts between individuals,
and characterize the fundamental quantities that impact any general process
taking place upon them. Furthermore, we introduce different randomizing
strategies that allow us to single out the role of the different properties of
the empirical networks. We show that the random walk exploration is slower on
temporal networks than it is on the aggregate projected network, even when the
time is properly rescaled. In particular, we point out that a fundamental role
is played by the temporal correlations between consecutive contacts present in
the data. Finally, we address the consequences of the intrinsically limited
duration of many real world dynamical networks. Considering the fundamental
prototypical role of the random walk process, we believe that these results
could help to shed light on the behavior of more complex dynamics on temporally
evolving networks.
