Eradicating Catastrophic Collapse in Interdependent Networks via Reinforced Nodes

TL;DR

This paper introduces a generalized percolation model with reinforced nodes in interdependent networks, showing that a small fraction of such nodes can prevent catastrophic failures and improve network resilience.

Contribution

It proposes a new model incorporating reinforced nodes in interdependent networks, providing analytical and simulation results on the minimal reinforcement needed to avoid abrupt collapses.

Findings

Reinforcing less than 18% of nodes prevents catastrophic collapse.

A universal upper bound of 17.56% reinforcement applies across various network types.

The model extends to networks of networks, enhancing resilience strategies.

Abstract

In interdependent networks, it is usually assumed, based on percolation theory, that nodes become nonfunctional if they lose connection to the network giant component. However, in reality, some nodes, equipped with alternative resources, together with their connected neighbors can still be functioning once disconnected from the giant component. Here we propose and study a generalized percolation model that introduces a fraction of reinforced nodes in the interdependent networks that can function and support their neighborhood. We analyze, both analytically and via simulations, the order parameter$-$the functioning component$-$comprising both the giant component and smaller components that include at least one reinforced node. Remarkably, we find that for interdependent networks, we need to reinforce only a small fraction of nodes to prevent abrupt catastrophic collapses. Moreover, we find that the universal upper bound of this fraction is 0.1756 for two interdependent Erd\H{o}s-R\'{e}nyi (ER) networks, regular-random (RR) networks and scale-free (SF) networks with large average degrees. We also generalize our theory to interdependent networks of networks (NON). Our findings might yield insight for designing resilient interdependent infrastructure networks.