Topological structures are consistently overestimated in functional complex networks

TL;DR

This paper demonstrates that traditional methods overestimate topological structures in functional networks, especially with short data, and proposes a Bayesian approach to correct this bias, validated on synthetic and brain data.

Contribution

It introduces a Bayesian inference method for reconstructing functional networks that accounts for uncertainty, reducing overestimation of topological features.

Findings

Frequentist methods overestimate network topology due to ignoring link uncertainty.

Bayesian approach reduces topological overestimation in synthetic and real brain networks.

Bias increases with shorter time series, indicating a resolution limit.

Abstract

Functional complex networks have meant a pivotal change in the way we understand complex systems, being the most outstanding one the human brain. These networks have classically been reconstructed using a frequentist approach that, while simple, completely disregards the uncertainty that derives from data finiteness. We here provide an alternative solution based on Bayesian inference, with link weights treated as random variables described by probability distributions, from which ensembles of networks are sampled. By using both statistical and topological considerations, we prove that the role played by links' uncertainty is equivalent to the introduction of a random rewiring, whose omission leads to a consistent overestimation of topological structures. We further show that this bias is enhanced in short time series, suggesting the existence of a theoretical time resolution limit for obtaining reliable structures. We also propose a simple sampling process for correcting topological values obtained in frequentist networks. We finally validate these concepts through synthetic and real network examples, the latter representing the brain electrical activity of a group of people during a cognitive task.