Spatial small-world networks: A wiring-cost perspective

TL;DR

This paper explores how the distribution of wiring lengths in spatial small-world networks influences their topology, flow distribution, and robustness, highlighting that certain length distributions yield optimal network properties.

Contribution

It demonstrates that specific wiring-cost distributions, particularly power-law forms, promote small-world features and robustness in spatial networks.

Findings

Power-law length distributions favor small-world topology.

Certain distributions improve network robustness.

Wiring costs significantly impact flow and connectivity.

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^{-\alpha} 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.