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Percolation Theory on Interdependent Networks Based on Epidemic Spreading
Seung-Woo Son, Golnoosh Bizhani, Claire Christensen, Peter Grassberger, Maya Paczuski
TL;DR
The paper addresses cumbersome cascade-based analyses of percolation on interdependent networks. It recasts the problem as epidemic spreading using order-parameter equations, obtaining transitions for several network types while limiting the theory to large, random, locally treelike networks.
Problem
Cascade-based descriptions of interdependent-network percolation are mathematically cumbersome, motivating a more transparent theory for systems with network interdependence.
Method
The paper omits explicit cascades and treats interdependent and dependency-network percolation as epidemic spreading, using modular order-parameter equations.
Results
The resulting equations reproduce continuous transitions for ordinary percolation and dependent regimes, discontinuous transitions for fully interdependent networks, and tricritical crossover behavior for partial dependency.
Takeaways & Limitations
The epidemic-spreading formulation extends to multiple interdependent networks and dependency links without explicitly modeling failure cascades.
Takeaways & Limitations
The theory applies only to large, random, locally treelike networks and does not provide an analytical theory for correlated or spatially embedded interdependent networks.
Abstract
from arXiv · showhide
We consider percolation on interdependent locally treelike networks, recently introduced by Buldyrev et al., Nature 464, 1025 (2010), 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.