title: Effective centrality and explosive synchronization in complex networks.
abstract: Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. We here propose an effective network whose topological properties reflect the interplay between the topology and dynamics of the original network. On that basis, we are able to introduce the effective centrality, a measure that quantifies the role and importance of each network's node in the synchronization process. In particular, in the context of explosive synchronization, we use such a measure to assess the propensity of a graph to sustain an irreversible transition to synchronization. We furthermore discuss a strategy to induce the explosive behavior in a generic network, by acting only upon a fraction of its nodes.
authors.affiliation: Center for Biomedical Technology, Univ. Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
authors.forename: A
authors.initials: A
authors.lastname: Navas
authors.affiliation: Department of Applied Mathematics, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain.
authors.forename: J A
authors.initials: JA
authors.lastname: Villacorta-Atienza
authors.affiliation: Center for Biomedical Technology, Univ. Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.|Complex Systems Group & GISC, Univ. Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
authors.forename: I
authors.initials: I
authors.lastname: Leyva
authors.affiliation: Center for Biomedical Technology, Univ. Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.|Complex Systems Group & GISC, Univ. Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
authors.forename: J A
authors.initials: JA
authors.lastname: Almendral
authors.affiliation: Center for Biomedical Technology, Univ. Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.|Complex Systems Group & GISC, Univ. Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
authors.forename: I
authors.initials: I
authors.lastname: Sendiña-Nadal
authors.affiliation: CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.|Embassy of Italy in Israel, Trade Tower, 25 Hamered St., 68125 Tel Aviv, Israel.
authors.forename: S
authors.initials: S
authors.lastname: Boccaletti