HodgeNet: Graph Neural Networks for Edge Data

Networks and network processes have emerged as powerful tools for modeling social interactions, disease propagation, and a variety of additional dynamics driven by relational structures. Recently, neural networks have been generalized to process data on graphs, thus being able to learn from the aforementioned network processes achieving cutting-edge performance in traditional tasks such as node classification and link prediction. However, these methods have all been formulated in a way suited only to data on the nodes of a graph. The application of these techniques to data supported on the edges of a graph, namely flow signals, has not been explored in detail. To bridge this gap, we propose the use of the so-called Hodge Laplacian combined with graph neural network architectures for the analysis of flow data. Specifically, we apply two graph neural network architectures to solve the problems of flow interpolation and source localization.