Percolation Theory on Interdependent Networks Based on Epidemic Spreading

TL;DR

This paper simplifies the analysis of percolation on interdependent networks by removing the need to explicitly model failure cascades, extending epidemic spreading theory to interconnected systems.

Contribution

It introduces a streamlined approach to interdependent network percolation that avoids complex cascade modeling, enabling easier extensions to multiple networks and dependency link structures.

Findings

Simplified percolation analysis on interdependent networks.

Framework directly based on an order parameter.

Method adaptable to multiple networks and dependency links.

Abstract

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.