  In designing and applying graph neural networks, we often fall into some
optimization pitfalls, the most deceptive of which is that we can only build a
deep model by solving over-smoothing. The fundamental reason is that we do not
understand how graph neural networks work. Stress graph drawing can offer a
unique viewpoint to message iteration in the graph, such as the root of the
over-smoothing problem lies in the inability of graph models to maintain an
ideal distance between nodes. We further elucidate the trigger conditions of
over-smoothing and propose Stress Graph Neural Networks. By introducing the
attractive and repulsive message passing from stress iteration, we show how to
build a deep model without preventing over-smoothing, how to use repulsive
information, and how to optimize the current message-passing scheme to
approximate the full stress message propagation. By performing different tasks
on 23 datasets, we verified the effectiveness of our attractive and repulsive
models and the derived relationship between stress iteration and graph neural
networks. We believe that stress graph drawing will be a popular resource for
understanding and designing graph neural networks.
