Network robustness and fragility: percolation on random graphs.

@article{Callaway2000NetworkRA,
  title={Network robustness and fragility: percolation on random graphs.},
  author={D. Callaway and M. Newman and S. Strogatz and D. Watts},
  journal={Physical review letters},
  year={2000},
  volume={85 25},
  pages={
          5468-71
        }
}
Recent work on the Internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes or links. Such deletions include, for example, the failure of Internet routers or power transmission lines. Percolation models on random graphs provide a simple representation of this process but have typically been limited to graphs with Poisson degree distribution at their vertices. Such graphs are quite unlike real-world… Expand
Critical percolation on random networks with prescribed degrees
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, onExpand
Percolation processes and wireless network resilience
TLDR
This work model this cascading failures problem in large-scale wireless networks, and shows that it is equivalent to a degree-dependent site percolation on random geometric graphs, and obtains analytical conditions for cascades. Expand
Percolation on correlated random networks
TLDR
It is derived that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks. Expand
Network Robustness Based on Inverse Percolation
TLDR
Percolation theory is used to assess the robustness of systems that can be modeled as general inhomogeneous random graphs as well as scale-free random graphs, and the random failures process of the network is mapped into an inverse percolation problem. Expand
Random Graphs as Models of Networks
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties.Expand
Percolation on sparse networks
TLDR
Percolation is reformulate as a message passing process and the resulting equations can be used to calculate the size of the percolating cluster and the average cluster size, finding them to be highly accurate when compared with direct numerical simulations. Expand
Wireless network resilience to degree-dependent and cascading node failures
  • Zhenning Kong, E. Yeh
  • Computer Science, Mathematics
  • 2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
  • 2009
TLDR
This work shows that the cascading failure problem for large-scale wireless networks is equivalent to a degree-dependent site percolation on random geometric graphs, and obtains analytical conditions for cascades in this model. Expand
L-hop percolation on networks with arbitrary degree distributions and its applications.
TLDR
Using the generating functions approach, analytic results on the percolation threshold as well as the mean size, and size distribution, of nongiant components of complex networks under such operations are presented. Expand
Robustness of complex networks with implications for consensus and contagion
TLDR
It is shown that the notions of connectivity and robustness coincide on these random graph models: the properties share the same threshold function in the Erdos-Rényi model, cannot be very different in the geometric random graph model, and are equivalent in the preferential attachment model. Expand
Percolation thresholds for robust network connectivity
TLDR
Four measures of robust network connectivity are defined, their interrelationships are explored, and the respective robust percolation thresholds for the 2D square lattice are evaluated. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 28 REFERENCES
Nature (London) 406
  • 378
  • 2000
Santa Fe Institute Report No
  • 00-11-062
  • 2000
  • 2000
Comput
  • Netw. 33, 309
  • 2000
Comput. Netw
  • Comput. Netw
  • 2000
Phys
  • Rev. E 62, 7059
  • 2000
Phys. Rev. E
  • Phys. Rev. E
  • 2000
Phys. Rev. Lett
  • Phys. Rev. Lett
  • 2000
Proc
  • Natl. Acad. Sci. U.S.A. 97, 11 149
  • 2000
Random Struct . Algorithms 6 , 161 ( 1995 ) ; Comb
  • Proc . Natl . Acad . Sci . U . S . A .
  • 2000
...
1
2
3
...