How is the human brain like the Internet, metabolic networks, relations among English words, US airport networks, Hungarian road networks

Navigable networks as Nash equilibria of navigation games

András Gulyás, József J. Bíró, Attila Kőrösi, Gábor Rétvári & Dmitri Krioukov

Nature Communications 6, Article number: 7651 doi:10.1038/ncomms8651

Received 04 December 2014 Accepted 26 May 2015 Published 03 July 2015

Abstract: Common sense suggests that networks are not random mazes of purposeless connections, but that these connections are organized so that networks can perform their functions well. One function common to many networks is targeted transport or navigation. Here, using game theory, we show that minimalistic networks designed to maximize the navigation efficiency at minimal cost share basic structural properties with real networks. These idealistic networks are Nash equilibria of a network construction game whose purpose is to find an optimal trade-off between the network cost and navigability. We show that these skeletons are present in the Internet, metabolic, English word, US airport, Hungarian road networks, and in a structural network of the human brain. The knowledge of these skeletons allows one to identify the minimal number of edges, by altering which one can efficiently improve or paralyse navigation in the network.