Percolation theory on interdependent networks based on epidemic spreading
Complexity Science Group, University of Calgary - Calgary T2N 1N4, Canada
2 FZ Jülich - D-52425 Jülich, Germany, EU
Accepted: 28 November 2011
We consider percolation on interdependent locally treelike networks, recently introduced by Buldyrev S. V. et al., Nature, 464 (2010) 1025, and demonstrate that the problem can be simplified conceptually by deleting all references to cascades of failures. Such cascades do exist, but their explicit treatment just complicates the theory —which is a straightforward extension of the usual epidemic spreading theory on a single network. Our method has the added benefits that it is directly formulated in terms of an order parameter and its modular structure can be easily extended to other problems, e.g. to any number of interdependent networks, or to networks with dependency links.
PACS: 64.60.ah – Percolation / 05.70.Jk – Critical point phenomena / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2012