  The invariance to permutations of the adjacency matrix, i.e., graph
isomorphism, is an overarching requirement for Graph Neural Networks (GNNs).
Conventionally, this prerequisite can be satisfied by the invariant operations
over node permutations when aggregating messages. However, such an invariant
manner may ignore the relationships among neighboring nodes, thereby hindering
the expressivity of GNNs. In this work, we devise an efficient
permutation-sensitive aggregation mechanism via permutation groups, capturing
pairwise correlations between neighboring nodes. We prove that our approach is
strictly more powerful than the 2-dimensional Weisfeiler-Lehman (2-WL) graph
isomorphism test and not less powerful than the 3-WL test. Moreover, we prove
that our approach achieves the linear sampling complexity. Comprehensive
experiments on multiple synthetic and real-world datasets demonstrate the
superiority of our model.
