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Network physiology describes the human body as a complex network of interacting organ systems. It has been applied successfully to determine topological changes in different sleep stages. However, the number of network links can quickly grow above the number of parameters that are typically analyzed with standard statistical methods. Artificial Neural Networks (ANNs) are a promising approach as they are successful in large parameter spaces, such as in digital imaging. On the other hand, ANN models do not provide an intrinsic approach to interpret their predictions, and they typically require large training data sets. Both aspects are critical in biomedical research. Medical decisions need to be explainable, and large data sets of quality assured patient and control data are rare. In this paper, different models for the classification of insomnia-a common sleep disorder-have been trained with 59 patients and age and gender matched controls, based on their physiological networks. Feature relevance evaluation is employed for all methods. For ANNs, the extrinsic interpretation method DeepLift is applied. The results are not identical across methods, but certain network links have been rated as relevant by all or most of the models. While ANNs show less classification accuracy (0.89) than advanced tree-based models (0.92 and 0.93), DeepLift provides an in-depth ANN interpretation with feature relevance scores for individual data samples. The analysis revealed modifications in the pulmonar, ocular, and cerebral subnetworks that have not been described before but are consistent with known findings on the physiological impact of insomnia.