  We study the problem of end-to-end learning from complex multigraphs with
potentially very large numbers of edges between two vertices, each edge labeled
with rich information. Examples range from communication networks to flights
between airports or financial transaction graphs. We propose Latent-Graph
Convolutional Networks (L-GCNs), which propagate information from these complex
edges to a latent adjacency tensor, after which further downstream tasks can be
performed, such as node classification. We evaluate the performance of several
variations of the model on two synthetic datasets simulating fraud in financial
transaction networks, ensuring the model must make use of edge labels in order
to achieve good classification performance. We find that allowing for nonlinear
interactions on a per-neighbor basis boosts performance significantly, while
showing promising results in an inductive setting. Finally, we demonstrate the
use of L-GCNs on real-world data in the form of an urban transportation
network.
