2012/09/03 by Víctor M. Preciado, Moez Draief, Preciado, Victor M. +3
Medicine · Physics and Astronomy · #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1209.0341
openalex publication_date 2012/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study how the behavior of viral spreading processes is influenced by local\nstructural properties of the network over which they propagate. For a wide\nvariety of spreading processes, the largest eigenvalue of the adjacency matrix\nof the network plays a key role on their global dynamical behavior. For many\nreal-world large-scale networks, it is unfeasible to exactly retrieve the\ncomplete network structure to compute its largest eigenvalue. Instead, one\nusually have access to myopic, egocentric views of the network structure, also\ncalled egonets. In this paper, we propose a mathematical framework, based on\nalgebraic graph theory and convex optimization, to study how local structural\nproperties of the network constrain the interval of possible values in which\nthe largest eigenvalue must lie. Based on this framework, we present a\ncomputationally efficient approach to find this interval from a collection of\negonets. Our numerical simulations show that, for several social and\ncommunication networks, local structural properties of the network strongly\nconstrain the location of the largest eigenvalue and the resulting spreading\ndynamics. From a practical point of view, our results can be used to dictate\nimmunization strategies to tame the spreading of a virus, or to design network\ntopologies that facilitate the spreading of information virally.\n