Using covariance of node states to design early warning signals for network dynamics

TL;DR

This paper investigates the effectiveness of using covariance between nodes as early warning signals for network regime shifts, finding that variance-based signals outperform covariance-based ones in predictive power.

Contribution

It introduces an analysis comparing covariance-based EWSs to variance-based EWSs, demonstrating the superiority of variance in network regime shift prediction.

Findings

Covariance-based EWSs are less effective than variance-based EWSs.

Variance-based signals outperform covariance signals in predicting regime shifts.

Diagonal covariance entries (variance) are preferred over off-diagonal entries for EWSs.

Abstract

Real-life systems often experience regime shifts. An early warning signal (EWS) is a quantity that attempts to anticipate such a regime shift. Because complex systems of practical interest showing regime shifts are often dynamics on networks, a research interest is to design EWSs for networks, including determining sentinel nodes that are useful for constructing high-quality EWSs. Previous work has shown that the sample variance is a viable EWS including in the case of networks. We explore the use of the sample covariance of two nodes, or sentinel node pairs, for improving EWSs for networks. We perform analytical calculations in four-node networks and numerical simulations in larger networks to find that the sample covariance and its combination over node pairs is inferior to the sample variance and its combination over nodes; the latter are previously proposed EWSs based on sentinel node selection. The present results support the predominant use of diagonal entries of the covariance matrix (i.e., variance) as opposed to off-diagonal entries in EWS construction.