  Graph neural networks (GNNs) have shown great ability in modeling graphs,
however, their performance would significantly degrade when there are noisy
edges connecting nodes from different classes. To alleviate negative effect of
noisy edges on neighborhood aggregation, some recent GNNs propose to predict
the label agreement between node pairs within a single network. However,
predicting the label agreement of edges across different networks has not been
investigated yet. Our work makes the pioneering attempt to study a novel
problem of cross-network homophilous and heterophilous edge classification
(CNHHEC), and proposes a novel domain-adaptive graph attention-supervised
network (DGASN) to effectively tackle the CNHHEC problem. Firstly, DGASN adopts
multi-head GAT as the GNN encoder, which jointly trains node embeddings and
edge embeddings via the node classification and edge classification losses. As
a result, label-discriminative embeddings can be obtained to distinguish
homophilous edges from heterophilous edges. In addition, DGASN applies direct
supervision on graph attention learning based on the observed edge labels from
the source network, thus lowering the negative effects of heterophilous edges
while enlarging the positive effects of homophilous edges during neighborhood
aggregation. To facilitate knowledge transfer across networks, DGASN employs
adversarial domain adaptation to mitigate domain divergence. Extensive
experiments on real-world benchmark datasets demonstrate that the proposed
DGASN achieves the state-of-the-art performance in CNHHEC.
