# 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…

## 92 Citations

### Cascades on clique-based graphs

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

An analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson, and how this technique can be used to study the effects of in-group bias in cascades on social networks is presented.

### Single-seed cascades on clustered networks

- Computer ScienceNetwork Science
- 2020

It is found that clustering impedes cascade propagation for networks of low average degree by reducing the connectivity of the network, but for networks with high average degree, the presence of small cycles makes cascades more likely.

### General and exact approach to percolation on random graphs.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A set of iterative equations that solve the exact distribution of the size and composition of components in finite-size quenched or random multitype graphs and define a very general random graph ensemble, which can be adapted to model interdependent graphs.

### Dynamics on Modular Networks with Heterogeneous Correlations

- Computer ScienceChaos
- 2014

An analytical approach is presented that allows one to analyze several types of binary dynamics operating on networks by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.

### The robustness of interdependent clustered networks

- BusinessArXiv
- 2012

It is found that clustering significantly increases the vulnerability of the system, which is represented by the increased value of the percolation threshold pc in interdependent networks.

### Impact of clustering on diffusions and contagions in random networks

- Mathematics, Computer ScienceInternational Conference on NETwork Games, Control and Optimization (NetGCooP 2011)
- 2011

A contagion model with threshold effects and conditions for the existence of a large cascade are obtained and a diffusion process with a given probability of contagion is analyzed.

### Network processes on clique-networks with high average degree: the limited eﬀect of higher-order structure

- Computer ScienceJournal of Physics: Complexity
- 2021

A random graph model that incorporates local clique structures, and thus deviates from the locally tree-like behavior of most standard random graph models is investigated, and derivations show that when the average degree of a vertex is large, the influence of the deviations from the local tree- like structure is small.

### of innovations in random clustered networks with overlapping communities

- Mathematics
- 2013

We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the…

### Mixing patterns in graphs with higher-order structure

- Computer Science
- 2022

This paper examines the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing and proposes a Monte Carlo graph generation algorithm to draw random networks from the ensemble of graphs with Monte Carlo statistics.

## References

SHOWING 1-10 OF 68 REFERENCES

### Cascades on correlated and modular random networks.

- PhysicsPhysical 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.

- Computer SciencePhysical 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.

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

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

- Computer ScienceProceedings 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.

- Computer SciencePhysical 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.

- Computer Science, PhysicsPhysical 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.

- MathematicsPhysical 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.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

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.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

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.

- PhysicsPhysical 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.