Robust design of geographical networks based on a population against failures and attacks

Robust and efficient design of networks on a realistic geographical space is one of the important issues to realize dependable communication systems. In this paper, based on a percolation theory and a geometric graph property, we investigate it in the following viewpoints: (1) network evolution according to a spatially inhomogeneous population, (2) optimal modality of degrees for the tolerant connectivity against both failures and attacks, and (3) decentralized routing within short paths. Furthermore, we point out the weakened tolerance by geographical constraints than the theoretical prediction, and propose a practical strategy to improve it by adding shortcut links between randomly chosen nodes. These properties of the bounded distance of path, the efficient routing, and the small modality to be robust will be useful for constructing future ad-hoc networks in wide area communication.