title: Degree-ordered percolation on a hierarchical scale-free network.
abstract: We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical (u,v) flower network with u ≤ v. Highest degree nodes are linked directly without intermediate nodes for u=1, while this is not the case for u ≠ 1. Using the renormalization-group-like procedure, we derive the recursion relations for the percolating probability and the percolation order parameter, from which the percolation threshold and the critical exponents are obtained. When u ≠ 1, the DOP critical behavior turns out to be identical to that of the bond percolation with a shifted nonzero percolation threshold. When u=1, the DOP and the bond percolation have the same vanishing percolation threshold but the critical behaviors are different. Implication to an epidemic spreading phenomenon is discussed.
authors.affiliation: Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea and School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
authors.forename: Hyun Keun
authors.initials: HK
authors.lastname: Lee
authors.affiliation: Department of Physics, University of Seoul, Seoul 130-743, Korea.
authors.forename: Pyoung-Seop
authors.initials: PS
authors.lastname: Shim
authors.affiliation: School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea and Department of Physics, University of Seoul, Seoul 130-743, Korea.
authors.forename: Jae Dong
authors.initials: JD
authors.lastname: Noh
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D015233:Models, Statistical; D018570:Risk Assessment