A world of networks

Modern life is reliant on networks, not least being the internet. Yet, the relationship between network structure and function is far from clear, meaning that networks can behave unpredictably.

The EU-funded COMPLEXNETROUTING (Efficient routing in the internet and other complex networks using hyperbolic metric spaces) project aimed to investigate. Specifically, the two-member consortium pursued the idea of hidden hyperbolic metric spaces guiding information transportation, but without needing knowledge of global topology. The group set three objectives aimed at testing the key ideas and constructing real networks. While the main focus was the internet, the project's concepts relate to all forms of networking. The four-year project concluded in early 2015.

Project goals were completed successfully. Main findings were as follows.

Hyperbolic geometries are most similar to real network topologies. The trade-offs between popularity and similarity in fact shape the structure and dynamics of complex networks. Thus, the networks are random geometric graphs growing in hyperbolic spaces. Secondly, the results apply to technological networks, but also to other kinds of networks, including biological and social. Combining popularity and similarity of network nodes creates a hyperbolic geometry.

Finally, the project derived a systematic framework that maps a network to a hyperbolic space. The resulting framework, applied to the internet, produced meaningful results. The performance of greedy forwarding, using the framework, is about 90 % of optimal. The framework can also predict missing and future links in real networks, and shows how communities evolve. The results have implications for a redesigned internet architecture.

The project revealed new aspects as to the workings of complex networks.