# Geometric correlations mitigate the extreme vulnerability of multiplex networks against targeted attacks

## TL;DR

This paper demonstrates that geometric correlations in multiplex networks significantly enhance their robustness against targeted attacks, transforming their failure dynamics from abrupt to gradual, which is crucial for designing resilient systems.

## Contribution

It reveals that hidden interlayer geometric correlations are key to the robustness of multiplex networks against targeted attacks, a novel insight into network resilience.

## Key findings

- Geometric correlations predict network robustness.
- Without geometric correlations, networks fail abruptly.
- With geometric correlations, failure is gradual and multistep.

## Abstract

We show that real multiplex networks are unexpectedly robust against targeted attacks on high degree nodes, and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.