Unraveling Spurious Properties of Interaction Networks with Tailored Random Networks

TL;DR

This paper examines how finite data and analysis methods can create misleading network topologies in interaction networks derived from multivariate time series, proposing tailored random networks to distinguish genuine from spurious properties.

Contribution

It introduces tailored random networks that account for finite data effects, improving the interpretation of interaction network properties in empirical data analysis.

Findings

Finite data limits reliability of interdependence estimators.

Interaction networks can exhibit spurious small-world properties.

Tailored random networks help differentiate true network features from artifacts.

Abstract

We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erd\H{o}s-R\'{e}nyi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures - known for their complex spatial and temporal dynamics - we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.