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Understanding phases of water molecules based on local structure is essential for understanding their anomalous properties. However, due to complicated structural motifs formed via hydrogen bonds, conventional order parameters represent the water molecules incompletely. In this paper, we develop a GCIceNet, which automatically generates machine-based order parameters for classifying the phases of the water molecules via supervised and unsupervised learning. Multiple graph convolutional layers in the GCIceNet can learn topological informations of the complex hydrogen bond networks. It shows a substantial improvement of accuracy for predicting the phase of water molecules in the bulk system and the ice/vapor interface system. A relative importance analysis shows that the GCIceNet can capture the structural features of the given system hidden in the input data. Augmented with the vast amount of data provided by molecular dynamics simulations, the GCIceNet is expected to serve as a powerful tool for the fields of glassy liquids and hydration layers around biomolecules.