  Graph Convolutional Networks (GCNs) have been extensively used to classify
vertices in graphs and have been shown to outperform other vertex
classification methods. GCNs have been extended to graph classification tasks
(GCT). In GCT, graphs with different numbers of edges and vertices belong to
different classes, and one attempts to predict the graph class. GCN based GCT
have mostly used pooling and attention-based models. The accuracy of existing
GCT methods is still limited. We here propose a novel solution combining GCN,
methods from knowledge graphs, and a new self-regularized activation function
to significantly improve the accuracy of the GCN based GCT. We present
quadratic GCN (QGCN) - A GCN formalism with a quadratic layer. Such a layer
produces an output with fixed dimensions, independent of the graph vertex
number. We applied this method to a wide range of graph classification
problems, and show that when using a self regularized activation function, QGCN
outperforms the state of the art methods for all graph classification tasks
tested with or without external input on each graph. The code for QGCN is
available at: https://github.com/Unknown-Data/QGCN .
