• Corpus ID: 118533963

Sandpile cascades on interacting tree-like networks

@article{Brummitt2010SandpileCO,
  title={Sandpile cascades on interacting tree-like networks},
  author={Charles D. Brummitt and Raissa M. D’Souza and Elizabeth A. Leicht},
  journal={arXiv: Disordered Systems and Neural Networks},
  year={2010}
}
The vulnerability of an isolated network to cascades is fundamentally affected by its interactions with other networks. Motivated by failures cascading among electrical grids, we study the Bak-Tang-Wiesenfeld sandpile model on two sparsely-coupled random regular graphs. By approximating avalanches (cascades) as a multi-type branching process and using a generalization of Lagrange's expansion to multiple variables, we calculate the distribution of avalanche sizes within each network. Due to… 

Figures and Tables from this paper

Multilayer networks
TLDR
The history of multilayer networks (and related concepts) is discussed and the exploding body of work on such networks is reviewed and attempts to generalize single-layer-network diagnostics to multilayers networks are reviewed.
The Effect of Clustering-Based and Degree-Based Weighting on Robustness in Symmetrically Coupled Heterogeneous Interdependent Networks
  • Yuzhuo Qiu
  • Mathematics, Computer Science
    2013 IEEE International Conference on Systems, Man, and Cybernetics
  • 2013
TLDR
It is demonstrated that both the clustering-based and degree-based weighting scheme outweigh random weighting on robustness against the cascade of load failures in the symmetrically coupled interdependent networks.

References

SHOWING 1-10 OF 49 REFERENCES
Catastrophic cascade of failures in interdependent networks
TLDR
This work develops a framework for understanding the robustness of interacting networks subject to cascading failures and presents exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks.
Percolation on interacting networks
Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst
Heterogeneous bond percolation on multitype networks with an application to epidemic dynamics.
TLDR
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.
Hierarchical structure and the prediction of missing links in networks
TLDR
This work presents a general technique for inferring hierarchical structure from network data and shows that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks.
Sandpile on scale-free networks.
TLDR
This work investigates the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, finding that the avalanche size distribution follows a power law with an exponent tau.
Error and attack tolerance of complex networks
TLDR
This work represents communication/transportation systems as networks and studies their ability to resist failures simulated as the breakdown of a group of nodes of the network chosen at random (chosen accordingly to degree or load).
Ja n 20 04 Sandpile avalanche dynamics on scale-free networks
Avalanche dynamics is an indispensable feature of complex s ystems. Here we study the self-organized critical dynamics of avalanches on scale-f re networks with degree exponent γ through the
Communication and correlation among communities.
  • M. Ostilli, J. Mendes
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
TLDR
It is proved that, among the communities, a superposition principle applies and gives rise to a natural generalization of the effective field theory already presented, and how, from the relative susceptibilities, a natural and efficient method to detect the community structure of a generic network arises.
Organization of modular networks
TLDR
It is demonstrated that even a relatively small number of shortcuts unite the networks into one if the number of interlinks is any finite fraction of the total number of connections, and the intervertex distance distribution approaches a delta -function peaked form.
Sandpiles on Watts-Strogatz type small-worlds
We study a one-dimensional sandpile model in small-world networks with long-range links either by introducing them randomly to fixed connection topology (quenched randomness) or to temporary
...
1
2
3
4
5
...