Graph Reciprocal Neural Networks by Abstracting Node as Attribute

Graph neural network (GNN) can be formulated as the multiplication of the topology-related matrix (adjacency or Laplacian matrix) and node attribute matrix, i.e., operation in node-wise. Unfortunately, this unified formula reveals two inherent drawbacks. Firstly, the topology and node attribute are not reciprocal but biased. From employment, the topology information is repeatedly employed, while the node attribute is only used once. From parameterization perspective, the node attribute is parameterized with highly expressive MLPs, while topology is not. Secondly, the graph topology can not be fully explored. Only the local pairwise relation is explored, but the mesoscopic community structure, which is one of the most prominent characteristics of networks, is ignored. To alleviate these issues, this paper proposes the Graph Reciprocal Network (GRN) by treating node attribute and topology reciprocal. Firstly, it is illustrated that the node can be regarded and utilized as another kind of attribute. Secondly, a novel node representation scheme is proposed from the theory of Quadratic Networks, with a theoretical guarantee of the fine-grained element-wise product of the representations of the topology and attribute. Extensive experiments demonstrate the superior performance and robustness of the proposed GRN.