Cascades on a class of clustered random networks

@article{Hackett2011CascadesOA,
  title={Cascades on a class of clustered random networks},
  author={Adam Hackett and Sergey Melnik and James P. Gleeson},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2011},
  volume={83 5 Pt 2},
  pages={
          056107
        }
}
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced previously in [M. E. J. Newman, Phys. Rev. Lett. 103, 058701 (2009)]. A condition for the existence of global cascades is derived as well as a general criterion that determines whether increasing the level of clustering will increase, or decrease, the expected cascade size… 

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References

SHOWING 1-10 OF 68 REFERENCES

Cascades on correlated and modular random networks.

  • J. Gleeson
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
An analytical approach to determining the mean avalanche size in a broad class of dynamical models on random networks is introduced. Previous results on percolation transitions and epidemic sizes are

Analytical results for bond percolation and k-core sizes on clustered networks.

  • J. GleesonS. Melnik
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
An analytical approach to calculating bond percolation thresholds, sizes of k-cores, and sizes of giant connected components on structured random networks with nonzero clustering is presented. The

Seed size strongly affects cascades on random networks.

It is demonstrated that the low- z transition may in fact be discontinuous in certain parameter regimes, and connections between these results and the zero-temperature random-field Ising model on random graphs are discussed.

A simple model of global cascades on random networks

  • D. Watts
  • Computer Science
    Proceedings of the National Academy of Sciences of the United States of America
  • 2002
It is shown that heterogeneity plays an ambiguous role in determining a system's stability: increasingly heterogeneous thresholds make the system more vulnerable to global cascades; but anincreasingly heterogeneous degree distribution makes it less vulnerable.

Random graphs with clustering.

  • M. Newman
  • Computer Science
    Physical review letters
  • 2009
It is shown how standard random-graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant components forms, and position ofThe phase transition for percolation on the network.

Bond percolation on a class of clustered random networks.

  • J. Gleeson
  • Computer Science, Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with nonzero clustering. The network's degree

Component sizes in networks with arbitrary degree distributions.

  • M. Newman
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
An exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions is given and it is shown that the component size distribution itself follows a power law everywhere below the phase transition at which a giant component forms, but takes an exponential form when a giant components is present.

How clustering affects the bond percolation threshold in complex networks.

Modelling highly clustered networks shows the presence of triangles in these model networks is shown to lead to a larger bond percolation threshold, compared to the threshold in an unclustered network with the same degree distribution and correlation structure.

Propagation dynamics on networks featuring complex topologies.

A mean-field description is used to coherently couple the dynamics of the network elements and their recurrent topological patterns and it is demonstrated that the model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.

Mean size of avalanches on directed random networks with arbitrary degree distributions.

  • J. Gleeson
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
It is shown here that the damage propagation function method may be used whenever the in-degree and out- Degree of network nodes are independently distributed; in particular, it is not necessary that the out-degree distribution be Poisson.
...