Recovery of contour nodes in interdependent directed networks

TL;DR

This paper develops an analytical framework for recovery strategies in interdependent directed networks, revealing phase transitions between collapse and recovery, and demonstrating resource-efficient targeted interventions on empirical data.

Contribution

It introduces a novel analytical model for recovery in interdependent directed networks with dependency links, identifying phase transitions and demonstrating effectiveness on real data.

Findings

Identifies three phases: collapse, recovery, and resilience.

Shows targeted recovery can prevent total system collapse.

Demonstrates resource savings over random recovery strategies.

Abstract

Extensive research has focused on studying the robustness of interdependent non-directed networks and the design of mitigation strategies aimed at reducing disruptions caused by cascading failures. However, real systems such as power and communication networks are directed, which underscores the necessity of broadening the analysis by including directed networks. In this work, we develop an analytical framework to study a recovery strategy in two interdependent directed networks in which a fraction $q$ of nodes in each network have single dependencies with nodes in the other network. Following the random failure of nodes that leaves a fraction $p$ intact, we repair a fraction of nodes that are neighbors of the giant strongly connected component of each network with probability or recovery success rate $\gamma$. Our analysis reveals an abrupt transition between total system collapse and complete recovery as $p$ is increased. As a consequence, we identify three distinct phases in the $(p, \gamma)$ parameter space: collapse despite intervention, recovery enabled by the strategy, and resilience without intervention. Moreover, we demonstrate our strategy on a system built from empirical data and find that it can save resources compared to a random recovery strategy. Our findings underscore the potential of targeted recovery strategies to enhance the robustness of real interdependent directed networks against cascading failures.