The network representation is becoming increasingly popular for the description of cardiovascular interactions based on the analysis of multiple simultaneously collected variables. However, the traditional methods to assess network links based on pairwise interaction measures cannot reveal high-order effects involving more than two nodes, and are not appropriate to infer the underlying network topology. To address these limitations, here we introduce a framework which combines the assessment of high-order interactions with statistical inference for the characterization of the functional links sustaining physiological networks. The framework develops information-theoretic measures quantifying how two nodes interact in a redundant or synergistic way with the rest of the network, and employs these measures for reconstructing the functional structure of the network. The measures are implemented for both static and dynamic networks mapped respectively by random variables and random processes using plug-in and model-based entropy estimators. The validation on theoretical and numerical simulated networks documents the ability of the framework to represent high-order interactions as networks and to detect statistical structures associated to cascade, common drive and common target effects. The application to cardiovascular networks mapped by the beat-to-beat variability of heart rate, respiration, arterial pressure, cardiac output and vascular resistance allowed noninvasive characterization of several mechanisms of cardiovascular control operating in resting state and during orthostatic stress. Our approach brings to new comprehensive assessment of physiological interactions and complements existing strategies for the classification of pathophysiological states.

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