# Layer degradation triggers an abrupt structural transition in multiplex networks

## TL;DR

This paper investigates how gradual or discrete loss of link weights in multiplex networks causes an abrupt structural transition, characterized by a sudden change in algebraic connectivity, with implications for network robustness.

## Contribution

It introduces the concept of layer degradation triggering a phase transition in multiplex networks and derives the exact critical value of intra-layer link weights for this transition.

## Key findings

- Layer degradation causes an abrupt change in algebraic connectivity.
- Identifies the critical intra-layer link weight at transition point.
- Connects layer degradation transition to inter-layer coupling variation.

## Abstract

Network robustness is a central point in network science, both from a theoretical and a practical point of view. In this paper, we show that layer degradation, understood as the continuous or discrete loss of links' weight, triggers a structural transition revealed by an abrupt change in the algebraic connectivity of the graph. Unlike traditional single layer networks, multiplex networks exist in two phases, one in which the system is protected from link failures in some of its layers and one in which all the system senses the failure happening in one single layer. We also give the exact critical value of the weight of the intra-layer links at which the transition occurs for continuous layer degradation and its relation to the value of the coupling between layers. This relation allows us to reveal the connection between the transition observed under layer degradation and the one observed under the variation of the coupling between layers.