  Most graph neural networks follow the message passing mechanism. However, it
faces the over-smoothing problem when multiple times of message passing is
applied to a graph, causing indistinguishable node representations and prevents
the model to effectively learn dependencies between farther-away nodes. On the
other hand, features of neighboring nodes with different labels are likely to
be falsely mixed, resulting in the heterophily problem. In this work, we
propose to order the messages passing into the node representation, with
specific blocks of neurons targeted for message passing within specific hops.
This is achieved by aligning the hierarchy of the rooted-tree of a central node
with the ordered neurons in its node representation. Experimental results on an
extensive set of datasets show that our model can simultaneously achieve the
state-of-the-art in both homophily and heterophily settings, without any
targeted design. Moreover, its performance maintains pretty well while the
model becomes really deep, effectively preventing the over-smoothing problem.
Finally, visualizing the gating vectors shows that our model learns to behave
differently between homophily and heterophily settings, providing an
explainable graph neural model.
