  The common sense suggests that networks are not random mazes of purposeless
connections, but that these connections are organised so that networks can
perform their functions well. One function common to many networks is targeted
transport or navigation. Using game theory, here we show that minimalistic
networks designed to maximise 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.
