Network robustness and fragility: percolation on random graphs.

  title={Network robustness and fragility: percolation on random graphs.},
  author={Duncan S. Callaway and Mark E. J. Newman and Steven H. Strogatz and Duncan J. Watts},
  journal={Physical review letters},
  volume={85 25},
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… 

Figures from this paper

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, on

Percolation on correlated random networks

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.

Percolation processes and wireless network resilience

  • Z. KongE. Yeh
  • Computer Science
    2008 Information Theory and Applications Workshop
  • 2008
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.

Network Robustness Based on Inverse Percolation

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.

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.

Percolation on sparse networks

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.

L-hop percolation on networks with arbitrary degree distributions and its applications.

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.

Percolation thresholds for robust network connectivity

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.

Heterogeneous micro-structure of percolation in sparse networks

Using the message-passing formulation of percolation, considerable variation is discovered across the network in the probability of a particular node to remain part of the giant component, and in the expected size of small clusters containing that node.

The Effect of Random Edge Removal on Network Degree Sequence

This work examines what happens to a graph's degree structure under edge failures where the edges are removed independently with identical probabilities, and derives asymptotic results for almost any degree sequence of interest.



Santa Fe Institute Report No

  • 00-11-062
  • 2000

Nature 401

  • 131
  • 1999

Nature 406

  • 378
  • 2000

Nature (London) 401

  • 131
  • 1999

and L

  • Lu, in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing
  • 2000

in press, also cond-mat/0005264) except for the cluster size distribution, which was calculated using ordinary depth-first search. The value of qc was assumed equal to the value of q at

  • Phys. Rev. Lett


  • Natl. Acad. Sci. U.S.A. 97, 11 149
  • 2000

Comput. Netw

  • Comput. Netw
  • 2000


  • Netw. 33, 309
  • 2000

in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing

  • Portland, OR, 2000
  • 2000