title: Cascading failures in interdependent networks with finite functional components.
abstract: We present a cascading failure model of two interdependent networks in which functional nodes belong to components of size greater than or equal to s. We find theoretically and via simulation that in complex networks with random dependency links the transition is first order for s≥3 and continuous for s=2. We also study interdependent lattices with a distance constraint r in the dependency links and find that increasing r moves the system from a regime without a phase transition to one with a second-order transition. As r continues to increase, the system collapses in a first-order transition. Each regime is associated with a different structure of domain formation of functional nodes.
authors.affiliation: Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR)-Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350, (7600) Mar del Plata, Argentina.
authors.forename: M A
authors.initials: MA
authors.lastname: Di Muro
authors.affiliation: Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA.
authors.forename: S V
authors.initials: SV
authors.lastname: Buldyrev
authors.affiliation: Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: H E
authors.initials: HE
authors.lastname: Stanley
authors.affiliation: Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR)-Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata-CONICET, Funes 3350, (7600) Mar del Plata, Argentina.|Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: L A
authors.initials: LA
authors.lastname: Braunstein