In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this problem leads to a new type of percolation transition, here termed a {\it network observability transition}, which we solve analytically for the configuration model. We also demonstrate a dual role of the network's community structure, which both facilitates optimal measurement placement and renders the networks substantially more sensitive to `observability attacks'. Aside from their immediate implications for the development of smart grids, these results provide insights into decentralized biological, social, and technological networks.
@article{arxiv.1301.5916,
title = {Network Observability Transitions},
author = {Yang Yang and Jianhui Wang and Adilson E. Motter},
journal= {arXiv preprint arXiv:1301.5916},
year = {2013}
}