Triple Point in Correlated Interdependent Networks

TL;DR

This paper models the failure dynamics in interdependent networks, revealing a phase diagram with a triple point that distinguishes between functional and non-functional states, especially considering high-degree node interdependencies.

Contribution

It introduces dynamic equations for interdependent networks that incorporate arbitrary interdependency patterns and analyzes the rich phase diagram including a triple point.

Findings

Failure cascades depend on interdependency patterns.

High-degree node interdependence influences network robustness.

A phase diagram with a triple point characterizes different network states.

Abstract

Many real-world networks depend on other networks, often in non-trivial ways, to maintain their functionality. These interdependent "networks of networks" are often extremely fragile. When a fraction $1-p$ of nodes in one network randomly fails, the damage propagates to nodes in networks that are interdependent and a dynamic failure cascade occurs that affects the entire system. We present dynamic equations for two interdependent networks that allow us to reproduce the failure cascade for an arbitrary pattern of interdependency. We study the "rich club" effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction $\alpha$ of the higher degree nodes on each network. We find a rich phase diagram in the plane $p-\alpha$, with a triple point reminiscent of the triple point of liquids that separates a non-functional phase from two functional phases.