# Applicability of spatial early warning signals to complex network dynamics

## TL;DR

This paper explores how spatial early warning signals can predict tipping points in complex networks, finding that some signals work better than others.

## Contribution

The study evaluates six spatial early warning signals on various networks, revealing their performance differences and reliability.

## Key findings

- Coefficient of variation and spatial skewness outperform other early warning signals in many scenarios.
- Spatial EWSs are more reliable on complex networks than on square lattices.
- Performance of EWSs varies depending on the tipping scenario.

## Abstract

Early warning signals (EWSs) for complex dynamical systems aim to anticipate tipping points before they occur. While signals computed from time-series data, such as temporal variance, are useful for this task, they are costly to obtain in practice because they need many samples over time to calculate. Spatial EWSs use just a single sample per spatial location and aggregate the samples over space rather than time to try to mitigate this limitation. However, although many complex systems in nature and society form diverse networks, the performance of spatial EWSs is mostly unknown for general networks because the vast majority of studies of spatial EWSs have been on regular lattice networks. Therefore, we have carried out a comprehensive investigation of six major spatial EWSs on various networks. We find that the winning EWS depends on tipping scenarios, although the coefficient of variation and spatial skewness tend to outperform alternative EWSs. We also find that spatial EWSs behave in a drastically different manner between the square lattice and complex networks and tend to be more reliable for the latter than the former. The present results encourage further studies of spatial EWSs on complex networks.