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Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
Roni Parshani, Sergey V. Buldyrev, Shlomo Havlin
TL;DR
Real interdependent networks may have only a fraction of nodes dependent across networks, and failures can cascade through both. The paper models these cascades and shows that reducing coupling changes the percolation transition from first to second order at a critical point, where the order parameter scales with exponent β=1.
Problem
Real interdependent networks need not have every node dependent across networks, and cascading failures can fragment both networks.
Source: pp. 1–2Method
The authors model two randomly connected networks with fractions qA and qB of dependent nodes and analyze their iterative cascade process.
Source: p. 2Results
Reducing coupling changes the percolation transition from first to second order at a critical point, where the order parameter scales linearly with distance and β=1.
Source: p. 1Takeaways & Limitations
Even with weak coupling and a second-order transition, the networks still disintegrate through iterative cascading failures.
Source: p. 2
Abstract
from arXiv · showhide
We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on the nodes of network B and a fraction of the nodes in network B depends on the nodes of network A. Due to the coupling between the networks when nodes in one network fail they cause dependent nodes in the other network to also fail. This invokes an iterative cascade of failures in both networks. When a critical fraction of nodes fail the iterative process results in a percolation phase transition that completely fragments both networks. We show both analytically and numerically that reducing the coupling between the networks leads to a change from a first order percolation phase transition to a second order percolation transition at a critical point. The scaling of the percolation order parameter near the critical point is characterized by the critical exponent beta=1.