2016/07/25 by Yang Yang, Filippo Radicchi
Computer Science · Mathematics · Physics and Astronomy · #Ansatz #Applied mathematics #Artificial intelligence #Cluster (spacecraft) #Cluster analysis #Clustering coefficient #Complex Network Analysis Techniques #Computer science #Data Visualization and Analytics #Function (biology) #Mathematical optimization #Mathematics #Network topology #Nonlinear system #Observability #Observable #Opinion Dynamics and Social Influence #Physics #Scalability #Statistical physics #Theoretical computer science #Topology (electrical circuits) #cond-mat.stat-mech #cs.SI #physics.soc-ph
paper · pdf · doi:10.1103/physreve.94.030301
published as Phys. Rev. E 94, 030301 (2016) · 5 pages, 3 figures + appendix
arxiv created 2016/07/25 · openalex publication_date 2016/09/07 · arxiv updated 2016/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider the observability model in networks with arbitrary topologies. We introduce a system of coupled nonlinear equations, valid under the locally treelike 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.