title: k-core percolation on multiplex networks.
abstract: We generalize the theory of k-core percolation on complex networks to k-core percolation on multiplex networks, where k≡(k(1),k(2),...,k(M)). Multiplex networks can be defined as networks with vertices of one kind but M different types of edges, representing different types of interactions. For such networks, the k-core is defined as the largest subgraph in which each vertex has at least k(i) edges of each type, i=1,2,...,M. We derive self-consistency equations to obtain the birth points of the k-cores and their relative sizes for uncorrelated multiplex networks with an arbitrary degree distribution. To clarify our general results, we consider in detail multiplex networks with edges of two types and solve the equations in the particular case of Erdős-Rényi and scale-free multiplex networks. We find hybrid phase transitions at the emergence points of k-cores except the (1,1)-core for which the transition is continuous. We apply the k-core decomposition algorithm to air-transportation multiplex networks, composed of two layers, and obtain the size of (k(1),k(2))-cores.
authors.affiliation: Physics Department, Institute for Advanced Studies in Basic Sciences, 45195-1159 Zanjan, Iran.
authors.forename: N
authors.initials: N
authors.lastname: Azimi-Tafreshi
authors.affiliation: Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain and Instituto de Biocomputación y Física de los Sistemas Complejos (BIFI), Universidad de Zaragoza, E-50018 Zaragoza, Spain.
authors.forename: J
authors.initials: J
authors.lastname: Gómez-Gardeñes
authors.affiliation: Departamento de Física da Universidade de Aveiro & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal and A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia.
authors.forename: S N
authors.initials: SN
authors.lastname: Dorogovtsev
mesh_terms: D000401:Aircraft; D000465:Algorithms; D008962:Models, Theoretical; D044367:Phase Transition