  In real communication and transportation networks, the geographical positions
of nodes are very important for the efficiency and the tolerance of
connectivity. Considering spatially inhomogeneous positions of nodes according
to a population, we introduce a multi-scale quartered (MSQ) network that is
stochastically constructed by recursive subdivision of polygonal faces as a
self-similar tiling. It has several advantages: the robustness of connectivity,
the bounded short path lengths, and the shortest distance routing algorithm in
a distributive manner. Furthermore, we show that the MSQ network is more
efficient with shorter link lengths and more suitable with lower load for
avoiding traffic congestion than other geographical networks which have various
topologies ranging from river to scale-free networks. These results will be
useful for providing an insight into the future design of ad hoc network
infrastructures.
