From visibility graphs to cognition.
Frontiers in network physiology January 1, 2026 Sabin Gautam, Paolo Grigolini
The natural visibility graph method (NVGM) builds complex networks from time series, but earlier work overlooked conditions where the system deviates from ordinary ergodicity due to turbulent events with an inverse power law index μ ranging from 1 to ∞. For 2 < μ < 3, the non-ergodic signal becomes nearly indistinguishable from fractional Gaussian noise (FGN). Using diffusion entropy analysis (DEA) with stripes reveals that meditation significantly reduces the scaling δ. NVGM generates a homogeneous network. The analysis distinguishes sick from healthy patients: in healthy patients, stripes leave δ virtually unchanged, while in sick patients, stripes yield a significantly lower δ, suggesting their heartbeats contain an FGN contribution.