Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition

TL;DR

This paper investigates how decreasing the coupling strength between two interdependent networks transforms the percolation transition from abrupt (first order) to gradual (second order), with analytical and numerical evidence.

Contribution

It demonstrates analytically and numerically that reducing coupling strength changes the percolation transition order in interdependent networks.

Findings

Reducing coupling strength changes the transition from first to second order.

Critical exponent beta=1 characterizes the transition near the critical point.

A critical coupling point marks the change in transition type.

Abstract

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.