A graph similarity for deep learning

Graph neural networks (GNNs) have been successful in learning representations from graphs. Many popular GNNs follow the pattern of aggregate-transform: they aggregate the neighbors' attributes and then transform the results of aggregation with a learnable function. Analyses of these GNNs explain which pairs of non-identical graphs have different representations. However, we still lack an understanding of how similar these representations will be. We adopt kernel distance and propose transform-sum-cat as an alternative to aggregate-transform to reflect the continuous similarity between the node neighborhoods in the neighborhood aggregation.