# Biased percolation on scale-free networks.

@article{Hooyberghs2010BiasedPO, title={Biased percolation on scale-free networks.}, author={Hans Hooyberghs and Bert Van schaeybroeck and Andr{\'e} A. Moreira and J. S. Andrade and Hans J. Herrmann and Joseph O. Indekeu}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2010}, volume={81 1 Pt 1}, pages={ 011102 } }

Biased (degree-dependent) percolation was recently shown to provide strategies for turning robust networks fragile and vice versa. Here, we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes i and j to be retained is proportional to (k(i)k(j)(-alpha) with k(i) and k(j) the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their…

## Figures and Tables from this paper

## 27 Citations

### Degree-dependent network growth: from preferential attachment to explosive percolation.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

A simple model of network growth is presented by writing the dynamic equations for its macroscopic characteristics such as the degree distribution and degree correlations and introduces the exemplary linking rule pk∝k-α, with α between -1 and +∞.

### Measuring degree-dependent failure in scale-free networks of bipartite structure

- Computer ScienceInt. J. Simul. Process. Model.
- 2013

A clear division between robust regime and fragile regime can be extracted based on natural connectivity by tuning the exponent α, which is an average eigenvalue obtained from the graph spectrum, based on a recently proposed spectral measure, natural connectivity.

### Biased edge failure in scale-free networks based on natural connectivity

- Physics
- 2012

The natural connectivity is recently reported as a novel spectral measure of robustness in complex networks. It has a clear physical meaning and a simple mathematical formulation. In this article,…

### Percolation of aligned rigid rods on two-dimensional square lattices.

- Materials SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The results show that the percolation threshold exhibits a decreasing function when it is plotted as a function of the kmer size, and in the case of aligned kmers, the intersection points of the curves of R(L,k)(p) for different system sizes exhibit nonuniversal critical behavior, varying continuously with changes in the kmers size.

### The network asymmetry caused by the degree correlation and its effect on the bimodality in control

- Computer Science
- 2021

### Solving the speed and accuracy of box-covering problem in complex networks

- Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2019

### Degree correlation in scale-free graphs

- Computer ScienceArXiv
- 2013

We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady…

## References

SHOWING 1-10 OF 87 REFERENCES

### Criticality on networks with topology-dependent interactions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology by mapping gamma'=(gamma-mu)(1-mu) , which can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

### Percolation in directed scale-free networks.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

The percolation properties of directed scale-free networks with correlated in and out degree distributions are studied, derived from a phase diagram that indicates the existence of three regimes, determined by the values of the degree exponents.

### Inhomogeneous percolation models for spreading phenomena in random graphs

- Mathematics
- 2005

Percolation theory has been used a great deal in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description…

### Percolation critical exponents in scale-free networks.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

It is shown that for networks with 3<lambda<4, known to undergo a transition at a finite threshold of dilution, the critical exponents are different than the expected mean-field values of regular percolation in infinite dimensions.

### How to Make a Fragile Network Robust and Vice Versa

- MathematicsPhysical review letters
- 2009

Topologically biased failure in scale-free networks with a degree distribution P(k) proportional, variantk;-gamma is investigated, finding that the critical percolation threshold, at which global connectivity is lost, depends both on gamma and on alpha.

### Trading interactions for topology in scale-free networks.

- PhysicsPhysical review letters
- 2005

It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions, and the equivalence of topology and interaction holds for equilibrium and nonequilibrium systems.

### Heterogeneous bond percolation on multitype networks with an application to epidemic dynamics.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

It is shown that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models and also demonstrates that a number of previous models based on probability generating functions are special cases of the proposed formalism.

### Scale-free random graphs and Potts model

- Physics
- 2005

We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertexi has a prescribed weight Pi ∝ i-μ (0 < μ< 1) and an edge can connect verticesi andj with ratePiPj.…

### Second look at the spread of epidemics on networks.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

A semidirected random network is defined the authors call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population and can be defined for any time-homogeneous stochastic SIR model.

### Scale-free networks are ultrasmall.

- MathematicsPhysical review letters
- 2003

It is shown, using analytical arguments, that scale-free networks with 2<lambda<3 have a much smaller diameter, behaving as d approximately ln(ln(N), which is the lowest possible diameter.