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Efficient Navigation in Scale-Free Networks Embedded in Hyperbolic Metric Spaces
D. Krioukov, F. Papadopoulos, M. Boguñá, and A. Vahdat, "Efficient Navigation in Scale-Free Networks Embedded in Hyperbolic Metric Spaces", Tech. rep., arXiv cond-mat.stat-mech/0805.1266, May 2008.
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Efficient Navigation in Scale-Free Networks Embedded in Hyperbolic Metric Spaces

Dmitri Krioukov1
Fragkiskos Papadopoulos1
Marián Boguñá2
Amin Vahdat3
1

CAIDA, San Diego Supercomputer Center, University of California San Diego

2

Departament de Física Fonamental, Universitat de Barcelona

3

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.

Keywords: routing, topology
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