Mapping The Internet with Hyperbolic Geometry

'Hyperbolic map' of the internet will save it from COLLAPSE • The Register

International computer boffins are warning that the internet may "collapse" at some point within the next decade. They propose the use of a new routing method based on hyperbolic geometry, and have devised what they call a "hyperbolic atlas" of the entire net to aid in this plan.

Scientists draw up world atlas of the internet | Broadband | News | PC Pro

A transatlatic group of scientists have created the first geometric map of the internet in a bid to prepare for the mother of all online traffic jams.

The team - from universities in California, Barcelona and Cyprus - says its geometric “road atlas” of the internet could help improve web routing.

“We compare routing in the internet today to using a hypothetical road atlas, which is really just a long encoded list of road intersections and connections that would require drivers to pore through each line to plot a course to their destination without using any geographical, or geometrical, information which helps us navigate through the space in real life,” said Dmitri Krioukov, principal investigator of the project.

Krioukov is concerned that existing internet routing, which relies on only this topological information, is unsustainable.

Nature Communications | Article

Sustaining the Internet with hyperbolic mapping

Marián Boguñá, Fragkiskos Papadopoulos & Dmitri Krioukov

Nature Communications
Volume:1, Article number:62, doi:10.1038/ncomms1063


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.

Figure 1: Hyperbolic geometry at a glance. 

The exponentially growing number of people lying on the hyperbolic floor illustrates the exponential expansion of the hyperbolic space. 

Figure 2: Synthetic network in the Einsteinian model. 

 The modelled network illustrates the connection between hyperbolic geometry and scale-free topology of complex networks. All nodes lie within a hyperbolic disc of radius R. The radial node density grows exponentially with the distance from the origin O, whereas the average degree of nodes exponentially decreases.

  Figure 3: Hyperbolic atlas of the Internet.

The Internet's hyperbolic map is similar to a synthetic Einsteinian network in Figure 2. The size of AS nodes is proportional to the logarithm of their degrees.