Degree-ordered percolation on a hierarchical scale-free network

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.