Title: Quadratic GCN for graph classification. Abstract: Graph Convolutional Networks (GCN) have been extensively used to classify nodes in graphs and have been shown to outperform most other node classification methods. However, there are currently few GCN based formalism for graph classification tasks. In this task, graphs of different sizes (e.g. graphs representing different protein structures) belong to different classes, and one attempts to predict the graph class. 

We here propose a solution combing GCN and methods from knowledge graphs to produce a quadratic GCN (Q-GCN). We extend the GCN formalism by adding a quadratic layer to a standard GCN to classify full graphs. Such a layer produces an output with dimensions independent of the graph node number. This output is then passed through a softmax to classify full graphs. We applied this method to a wide range of graph classification problems and show that such a straightforward formalism outperforms state of the art methods for binary graph classification with or without external input on each graph. 
