Degree-ordered percolation on a hierarchical scale-free network

Hyun Keun Lee, Pyoung Seop Shim, Jae Dong Noh

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6 Scopus citations


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.

Original languageEnglish
Article number062816
JournalPhysical Review E
Issue number6
StatePublished - 27 Jun 2014


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