Degree-ordered percolation on a hierarchical scale-free network

作者：Lee Hyun Keun^*; Shim Pyoung Seop; Noh Jae Dong

来源：Physical Review E, 2014, 89(6): 062816.

DOI：10.1103/PhysRevE.89.062816

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 not equal 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 not equal 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.

• 出版日期2014-6-27