Observability transitions in correlated networks

TL;DR

This paper investigates how degree correlation in networks affects their observability, finding that negative correlation enhances observability and that optimized networks tend to have a hub-repulsive structure.

Contribution

It provides analytical and numerical insights into the role of degree correlation in network observability and introduces a method to optimize networks for maximum observability.

Findings

Negative degree correlation improves network observability.

Optimized networks exhibit hub-repulsive structures.

Networks with negative correlation have less hub-hub connectivity.

Abstract

Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components comprising the observable nodes is a major concern of the model. We analyze this model in random heterogeneous networks with degree correlation. With numerical simulations and analytical arguments based on generating functions, we find that negative degree correlation makes networks more observable. This result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors. Finally, we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component. Optimized networks have negative degree correlation induced by the resulting hub-repulsive structure; the largest hubs are rarely connected to each other, in contrast to the rich-club phenomenon of networks.