BACKGROUND: Contemporary deep learning approaches show cutting-edge performance in a variety of complex prediction tasks. Nonetheless, the application of deep learning in healthcare remains limited since deep learning methods are often considered as non-interpretable black-box models. However, the machine learning community made recent elaborations on interpretability methods explaining data point-specific decisions of deep learning techniques. We believe that such explanations can assist the need in personalized precision medicine decisions via explaining patient-specific predictions. METHODS: Layer-wise Relevance Propagation (LRP) is a technique to explain decisions of deep learning methods. It is widely used to interpret Convolutional Neural Networks (CNNs) applied on image data. Recently, CNNs started to extend towards non-Euclidean domains like graphs. Molecular networks are commonly represented as graphs detailing interactions between molecules. Gene expression data can be assigned to the vertices of these graphs. In other words, gene expression data can be structured by utilizing molecular network information as prior knowledge. Graph-CNNs can be applied to structured gene expression data, for example, to predict metastatic events in breast cancer. Therefore, there is a need for explanations showing which part of a molecular network is relevant for predicting an event, e.g., distant metastasis in cancer, for each individual patient. RESULTS: We extended the procedure of LRP to make it available for Graph-CNN and tested its applicability on a large breast cancer dataset. We present Graph Layer-wise Relevance Propagation (GLRP) as a new method to explain the decisions made by Graph-CNNs. We demonstrate a sanity check of the developed GLRP on a hand-written digits dataset and then apply the method on gene expression data. We show that GLRP provides patient-specific molecular subnetworks that largely agree with clinical knowledge and identify common as well as novel, and potentially druggable, drivers of tumor progression. CONCLUSIONS: The developed method could be potentially highly useful on interpreting classification results in the context of different omics data and prior knowledge molecular networks on the individual patient level, as for example in precision medicine approaches or a molecular tumor board.