In this paper, a novel multi-view methodology for graph based neural networks is proposed. A systematic and methodological adaptation of the key concepts of classical deep learning methods such as convolution, pooling and multi-view architectures is developed for the context of non-Euclidean manifolds. The aim of the proposed work is to present a novel multi-view graph convolution layer, as well as a new view pooling layer making use of: a) a new hybrid Laplacian that is adjusted based on feature distance metric learning, b) multiple trainable representations of a feature matrix of a graph, using trainable distance matrices, adapting the notion of views to graphs and c) a multi-view graph aggregation scheme called graph view pooling, in order to synthesize information from the multiple generated "views". The aforementioned layers are used in an end-to-end graph neural network architecture for graph classification and show competitive results to other state-of-the-art methods.