  The continuous interaction between brain regions "at rest" defines the
so-called resting state networks (RSN) which can be reconstructed from the
analysis of functional magnetic resonance imaging (fMRI) data. What dynamical
mechanism allows for a flexible large-scale organization of the RSN still
remains an important challenge. Here, three key novel properties of the RSN are
uncovered. First, the correlation length (i.e., the length at which correlation
between two regions vanishes) diverges with the cluster's size considered.
Second, this divergence it is observed also for measures of mutual information.
Third, the variance of the fMRI mean signal remains constant across the entire
range of observed clusters sizes, in contrast with naive expectations. The
unveiled scale invariance exposes the RSN optimal information-sharing
properties across very diverse networks sizes, architectures and functions,
which can be an important marker of healthy brain dynamics.
