  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.
