Observability transition in real networks

TL;DR

This paper develops a theoretical framework to predict the size of observable clusters in real-world networks, enabling efficient network monitoring and surveillance.

Contribution

It introduces a system of coupled nonlinear equations for arbitrary network topologies, validated on 95 real networks with high accuracy.

Findings

High prediction accuracy across diverse real networks

Effective modeling even with high clustering coefficients

Potential for scalable network monitoring algorithms

Abstract

We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally tree-like ansatz, to describe the size of the largest observable cluster as a function of the fraction of directly observable nodes present in the network. We perform a systematic analysis on 95 real-world graphs and compare our theoretical predictions with numerical simulations of the observability model. Our method provides almost perfect predictions in the majority of the cases, even for networks with very large values of the clustering coefficient. Potential applications of our theory include the development of efficient and scalable algorithms for real-time surveillance of social networks, and monitoring of technological networks.