Network Observability Transitions

Abstract

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.

References in corpus (10)

• Finding community structure in very large networks
• Random graphs with arbitrary degree distributions and their applications
• Network robustness and fragility: Percolation on random graphs
• Critical phenomena in complex networks
• Structural Vulnerability of the North American Power Grid
• "Explosive Percolation" Transition is Actually Continuous
• Robustness of the European power grids under intentional attack
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Networks in Motion
• Network resilience against intelligent attacks constrained by degree dependent node removal cost

Cited by in corpus (27)

• Control Principles of Complex Networks
• Percolation on complex networks: Theory and application
• Spectrum of Controlling and Observing Complex Networks
• Models for the modern power grid
• Networkcontrology
• Transdisciplinary electric power grid science
• Statistical Mechanics of the Minimum Dominating Set Problem
• Efficient network immunization under limited knowledge
• General and exact approach to percolation on random graphs
• Building Damage-Resilient Dominating Sets in Complex Networks against Random and Targeted Attacks
• The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation
• Dominating Scale-Free Networks Using Generalized Probabilistic Methods
• Observability transitions in correlated networks
• Improving power-grid systems via topological changes, or how self-organized criticality can help stability
• Minimal Dominating Set problem studied by simulated annealing and cavity method: Analytics and population dynamics
• Dynamical heterogeneity and universality of power-grids
• Coexistence of phases and the observability of random graphs
• Generalized minimum dominating set and application in automatic text summarization
• Improving Observability of Stochastic Complex Networks under the Supervision of Cognitive Dynamic Systems
• Observability transition in real networks
• Distinguishing Cell Phenotype Using Cell Epigenotype
• Observability transition in multiplex networks
• Observability transitions in clustered networks
• Target observation of complex networks
• Minimum Input Selection for Structural Controllability
• Observability of Nonlinear Complex Networks in the Presence of Symmetries: A Graphical Approach
• The Directed Dominating Set problem studied by cavity method: Warning propagation and population dynamics