Many real complex systems (e.g. communication, transportation, social and biological networks) are studied mathematically by using tools from graph theory. These systems, modeled as networks with weighted nodes and links, share many properties like that they are smallworld (short average distance), scale-free (adding now nodes does not change the main characteristics) and modular. These properties make them quite sensitive to cascading failures, as the failure of one or several nodes propagates easily and leads to a total collapse of the system. It is really important to prevent cascade failures like those which happened in recent years to the global router network, the European electrical network, and Facebook. Even illnesses can be associated to cascading failures in the human interactome (network of protein interactions). The approach to this problem in the current literature is essentially descriptive and based on simulations. With the aim to understand the cascading failure process and also to find efficient methods of protection, we will apply our graph theory and algorithmic knowledge to study it mathematically on model graphs and from real networks data the power grid and airport networks of EU and USA, the human interactome, and other public available data-. We plan to determine which vertex sets, graph invariants and parameters are relevant in the cascading failure process and we will propose methods and algorithms to control this catastrophic process. We are particularly interested in the role that vertices from different centrality sets (including domination sets) play as triggers of the failures and which changes would produce a resilient network. Our team has a relevant and complementary experience in different aspects of discrete mathematics (graph theory and algorithmics), with experience in technical and biological applications which should contribute to the success of this project.
Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020
Programa Estatal de Generación de Conocimiento y Fortalecimiento Científico y Tecnológico del Sistema de I+D+i
Subprograma Estatal de Generación de Conocimiento
Proyectos de I+D de generación de conocimiento (antigues EXC)