Sustaining the Internet with Hyperbolic Mapping

By Marián Boguñá, Fragkiskos Papadopoulos, Dmitri V. Krioukov. Nature Communications, 2010

483 citations recorded by the source corpus.

The Internet infrastructure is severely stressed. Rapidly growing overheads associated with the primary function of the Internet-routing information packets between any two computers in the world-cause concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade. In this paper, we present a method to map the Internet to a hyperbolic space. Guided by a constructed map, which we release with this paper, Internet routing exhibits scaling properties that are theoretically close to the best possible, thus resolving serious scaling limitations that the Internet faces today. Besides this immediate practical viability, our network mapping method can provide a different perspective on the community structure in complex networks.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b7bd9ee0254ae9ae2b7893b4661e4f057c3caf7a

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Citations in the corpus

Dimension of spatially embedded networks (2011, background): “In some cases, the assumption of a hyperbolic geometry instead of the Euclidean space may also be applicabl”
Hyperbolic Graph Neural Networks (2019, background): “Furthermore, [27, 6, 28] exploited the property of hyperbolic embeddings to embed tree-like graphs with low distortion, for greedy-path routing in large-scale communication networks.”
Network resilience (2020, unknown): “perbolic space [584].”
Poincaré Embeddings for Learning Hierarchical Representations (2017, background): “[4] proposed hyperbolic embeddings of the AS Internet topology to perform greedy shortest path routing in the embedding space.”
Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry (2018, methodology): “Furthermore, Kleinberg (2007) and Boguñá et al. (2010) proposed hyperbolic embeddings for greedy shortest-path routing in communication networks. Asta & Shalizi (2015) used hyperbolic embeddings of graph to compare the global structure of networks. Sun et al. (2015) proposed to learn representations”
Named data networking (2014, unknown): “For example, NLSR now supports a type of hyperbolic routing [16, 6] by disseminating hyperbolic coordinates in link state advertisements.”
Neural Embeddings of Graphs in Hyperbolic Space (2017, background): “Recent work from the field of complex networks has found that many interesting networks, such as the Internet [5] or academic citations [7, 8] can be well described by a framework with an underlying non-Euclidean hyperbolic geometry.”