Networks meet Geometry: A hyperbolic journey from the Internet to the Universe  Seminar

In the age of Information Technology, the Internet has become our primary communication system. One surprising fact about the Internet is that its complex architecture is the result of a self-organized process where individual agents interact locally without any central authority controlling its evolution. This turns the Internet into subject of truly scientific research. The Internet is now facing a serious scalability problem with its routing architecture. To route information packets to a given destination, Internet routers must communicate to maintain a coherent view of the global topology. The constantly increasing size and dynamics of the Internet thus leads to immense and quickly growing communication and information processing overhead, a major bottleneck in routing scalability causing concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade.

We assume that the Internet (and other complex networks) lives in a hidden metric space that shapes its topology. Discovery of this hidden metric space can then be used to greedily route information without detailed global knowledge of the network structure or organization. Interestingly, we find that hyperbolic geometry seems to describe very well the topology of the Internet and other real complex networks and that, in this geometry, greedy routing strategies achieves the optimal performance. In an unexpected turn of events, we find that the very same models that we use to model the Internet topology and evolution describe the causal structure of the de Sitter space-time --the asymptotic limit of our accelerating universe. These findings suggest that unexpectedly similar mechanisms may shape the large-scale structure and dynamics of complex systems as different as the brain, the Internet, and the universe.