T- Hop: Tensor representation of paths in graph convolutional networks

We describe a method for encoding path information in graphs into a 3-d tensor. We show a connection between the introduced path representation scheme and powered adjacency matrices. To alleviate the heavy computational demands of working with the 3-d tensor, we propose to apply dimensionality reduction on the depth axis of the tensor. We then describe our the reduced 3-d matrix can be parlayed into a plausible graph convolutional layer, by infusing it into an established graph convolutional network framework such as MixHop.