# Observability transition in multiplex networks

## TL;DR

This paper extends the observability model to multiplex networks, revealing that the transition to a large observable cluster is discontinuous in synthetic networks but smooth in real-world networks due to edge overlap.

## Contribution

It introduces a mathematical framework for observability in multiplex networks and analyzes the nature of the transition in synthetic versus real-world cases.

## Key findings

- Discontinuous observability transition in synthetic multiplex networks.
- Edge overlap in real-world networks smooths the transition.
- Mathematical framework valid under the treelike assumption.

## Abstract

We extend the observability model to multiplex networks. We present mathematical frameworks, valid under the treelike ansatz, able to describe the emergence of the macroscopic cluster of mutually observable nodes in both synthetic and real-world multiplex networks. We show that the observability transition in synthetic multiplex networks is discontinuous. In real-world multiplex networks instead, edge overlap among layers is responsible for the disappearance of any sign of abruptness in the emergence of the the macroscopic cluster of mutually observable nodes.