This hyperbolic map of the internet captures connections between systems on the network (Image: Marián Boguñá)

A novel map of the internet created by Marián Boguñá and colleagues at the University of Barcelona, Spain, could help make network glitches a thing of the past.

Boguñá squeezed the entire network into a disc using hyperbolic geometry, more familiar to us through the circular mosaic-like artworks of M. C. Escher.

Each square on the map is an “autonomous system” – a section of the network managed by a single body such as a national government or a service provider. The most well-connected systems are close to the centre, while the least connected are at the edges. The area of the hyperbolic plane grows exponentially with distance from the centre, so the edges of the map are “roomier” than the middle.


Like all good cartographers, Boguñá’s team hopes their map will help speed up navigation. At present each system routes traffic by referring to a table of all available network paths, but keeping this up to date is difficult as new paths keep coming on stream while others shut down.

Network coordinates

Boguñá’s map could do away with all this by providing “coordinates” for every system on the network. This turns routing traffic into a game of “pass the parcel”. Each system calculates in which “direction” the final destination of a packet of information lies, and simply relays each packet to the neighbour which lies closest to that direction – an approach called “greedy forwarding”.

Although the map simply shows the number of connections between each autonomous system, the geography of the hyperbolic internet map often reflects that of the real world – for example, a number of western European nations are clustered in one sector.

It might be assumed that Boguñá’s greedy-forwarding approach would route packets as effectively if applied to a map of the internet based on actual geographical relationships between systems rather than the hyperbolic map, which is based on the number of connections. However, the team’s simulations showed that applying the technique to a purely geographical map resulted in up to 86 per cent of traffic becoming trapped within the network. When using the hyperbolic map, just 3 per cent of traffic suffered this fate.

This trapping can happen when, for example, a packet reaches a point that is geographically close to its destination, but that lacks a direct link. If this happens, and the packet is forced to retrace its steps and visit the same autonomous system twice, the routing fails.

Journal reference: Nature Communications, DOI: 10.1038/ncomms1063)