Degree-ordered percolation on hierarchical scale-free network
arXiv:1403.2072 · doi:10.1103/PhysRevE.89.062816
Abstract
We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical 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 , the DOP critical behavior turns out to be identical to that of the bond percolation with a shifted nonzero percolation threshold. When , 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.
7 pages, 6 figures
References in corpus (20)
- Error and attack tolerance of complex networks
- Epidemic spreading in scale-free networks
- The spread of epidemic disease on networks
- Network robustness and fragility: Percolation on random graphs
- Resilience of the Internet to random breakdowns
- Epidemic dynamics and endemic states in complex networks
- Thresholds for epidemic spreading in networks
- Are randomly grown graphs really random?
- Localization and Spreading of Diseases in Complex Networks
- Stability and topology of scale-free networks under attack and defense strategies
- Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
- Fractal and Transfractal Recursive Scale-Free Nets
- Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network
- Percolation on correlated networks
- Percolation in Hierarchical Scale-Free Nets
- Epidemic Threshold of Susceptible-Infected-Susceptible Model on Complex Networks
- Percolation transition in networks with degree-degree correlation
- Biased Percolation on Scale-free Networks
- Hierarchical scale-free network is fragile against random failure
- Percolation transition in correlated static model