Spatial small-world networks: A wiring-cost perspective

Abstract

Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost associated to their length l, the corresponding distribution q(l) plays a crucial role. Uniform length distributions have received most attention despite indications that q(l) ~ l^{-α} exist, e.g. for integrated circuits, the Internet and cortical networks. Here we discuss for such systems the emergence of small-world topology, its relationship to the wiring costs, the distribution of flows as well as the robustness with respect to random failures and overload. The main finding is that the choice of such a distribution leads to favorable attributes in most of the investigated properties.