Relationship between mutual information and cross-correlation time scale of observability as measures of connectivity strength

The task of identifying and characterizing network structures out of experimentally observed time series is tackled by implementing different solutions, ranging from entropy-based techniques to the evaluation of the significance of observed correlation estimators. Among the metrics that belong to the first class, mutual information is of major importance due to the relative simplicity of implementation and its relying on the crucial concept of entropy. With regard to the second class, a method that allows us to assess the connectivity strength of a link in terms of a time scale of its observability via the significance estimate of measured cross correlation was recently shown to provide a reliable tool to study network structures. In this paper, we investigate the relationship between this last metric and mutual information by simultaneously assessing both metrics on large sets of data extracted from three experimental contexts, human brain magnetoencephalography, human brain electroencephalography, and surface wind measurements carried out on a small regional scale, as well as on simulated coupled, auto-regressive processes. We show that the relationship is well described by a power law and provide a theoretical explanation based on a simple noise and signal model. Besides further upholding the reliability of cross-correlation time scale of observability, the results show that the combined use of this metric and mutual information can be used as a valuable tool to identify and characterize connectivity links in a wide range of experimental contexts.