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arXiv · 1403.2072

Degree-ordered percolation on hierarchical scale-free network

Hyun Keun Lee·Pyoung-Seop Shim·Jae Dong Noh
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Abstract

We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical $(u,v)$ flower network. 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 $u\neq 1$, 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.

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Hyun Keun Lee, Pyoung-Seop Shim, Jae Dong Noh. 2014-03-09. Degree-ordered percolation on hierarchical scale-free network. https://doi.org/10.1103/physreve.89.062816

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