Abstract

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, remains 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.

Highlights

  • Information routing is one of the main tasks in many complex networks with a communication function

  • Navigation is expected to be substantially different in temporal networks than in static ones, few empirical or theoretical works have been devoted to study the impact of the temporal dimension on the navigability of complex systems[4,29,30]

  • We show that some real networks are ultranavigable, meaning that they remain highly navigable even when the network topology is strongly dynamic

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Summary

Introduction

Information routing is one of the main tasks in many complex networks with a communication function. Distances in the underlying hyperbolic geometry can guide greedy routing very efficiently in scale-free networks, meaning that the success probability of the process is extremely high, while the routing paths deviate only slightly from the topological shortest paths, following closely the geodesics in the hyperbolic plane[13] These advances in the understanding of the navigability of complex networks are framed within the traditional approach taking the structure of networks as static. This assumption has been recently challenged by the empirical observation of a temporal dimension in many natural and social systems[14,15,16,17], demonstrating that nodes and edges switch on and off with several time scales. Uncovering such mechanisms is a fundamental task, with a broad range of potential applications, for instance, in communication engineering[34] and system biology[35]

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