Efficient Navigation in Scale-Free Networks Embedded in Hyperbolic Metric Spaces

Dmitri Krioukov and Fragkiskos Papadopoulos
Cooperative Association for Internet Data Analysis - CAIDA
San Diego Supercomputer Center,
University of California, San Diego

Marián Boguñá
Departament de Física Fonamental,
Universitat de Barcelona, Martí i Franquès 1,
08028 Barcelona, Spain

Amin Vahdat
Department of Computer Science and Engineering,
University of California, San Diego

In this work we show that: i) the roughly hierarchical structure of complex networks is congruent with negatively curved geometries hidden beneath the observed topologies; ii) the most straightforward mapping of nodes to spaces of negative curvature naturally leads to the emergence of scale-free topologies; and iii) greedy routing on this embedding is efficient for these topologies, achieving both 100% reachability and optimal path lengths, even under dynamic network conditions. The critical important question left by this work is whether the topologies of real networks can be mapped into appropriate hidden hyperbolic metric spaces.