From brain to earth and climate systems: Small-world interaction networks or not?

Abstract

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with commonly used time series analysis based approaches to network characterization.

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• Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
• Identifying edges that facilitate the generation of extreme events in networked dynamical systems
• Ordinal methods for a characterization of evolving functional brain networks