Review of Bidirected Graph Neural Networks and Multidirected Graph Neural Networks

Graph theory studies the relationships among objects by modeling them as vertices (nodes) connected by edges [1-3]. Beyond the familiar undirected graph, there also exist directed, bidirected, and multidirected graphs, each encoding richer notions of orientation. Graph Neural Networks (GNNs) have emerged as a powerful framework in artificial intelligence [4-7], and recent work has extended them to directed graphs. In this paper, we further generalize directed GNNs to the bidirected and multidirected settings, developing Bidirected Graph Neural Networks and Multidirected Graph Neural Networks. We demonstrate how these extensions naturally incorporate more complex orientation patterns and anticipate that our results will spur new advances in GNN research.