  Information routing is one of the main tasks in many complex networks with a
communication function. Maps produced by embedding the networks in hyperbolic
space can assist this task enabling the implementation of efficient navigation
strategies. However, only static maps have been considered so far, while
navigation in more realistic situations, where the network structure may vary
in time, remain largely unexplored. Here, we analyze the navigability of real
networks by using greedy routing in hyperbolic space, where the nodes are
subject to a stochastic activation-inactivation dynamics. We find that such
dynamics enhances navigability with respect to the static case. Interestingly,
there exists an optimal intermediate activation value, which ensures the best
trade-off between the increase in the number of successful paths and a limited
growth of their length. Contrary to expectations, the enhanced navigability is
robust even when the most connected nodes inactivate with very high
probability. Finally, our results indicate that some real networks are
ultranavigable and remain highly navigable even if the network structure is
extremely unsteady. These findings have important implications for the design
and evaluation of efficient routing protocols that account for the temporal
nature of real complex networks.
