  Graph Neural Networks (GNNs) have achieved great success in processing graph
data by extracting and propagating structure-aware features. Existing GNN
research designs various propagation schemes to guide the aggregation of
neighbor information. Recently the field has advanced from local propagation
schemes that focus on local neighbors towards extended propagation schemes that
can directly deal with extended neighbors consisting of both local and
high-order neighbors. Despite the impressive performance, existing approaches
are still insufficient to build an efficient and learnable extended propagation
scheme that can adaptively adjust the influence of local and high-order
neighbors. This paper proposes an efficient yet effective end-to-end framework,
namely Contrastive Adaptive Propagation Graph Neural Networks (CAPGNN), to
address these issues by combining Personalized PageRank and attention
techniques. CAPGNN models the learnable extended propagation scheme with a
polynomial of a sparse local affinity matrix, where the polynomial relies on
Personalized PageRank to provide superior initial coefficients. In order to
adaptively adjust the influence of both local and high-order neighbors, a
coefficient-attention model is introduced to learn to adjust the coefficients
of the polynomial. In addition, we leverage self-supervised learning techniques
and design a negative-free entropy-aware contrastive loss to explicitly take
advantage of unlabeled data for training. We implement CAPGNN as two different
versions named CAPGCN and CAPGAT, which use static and dynamic sparse local
affinity matrices, respectively. Experiments on graph benchmark datasets
suggest that CAPGNN can consistently outperform or match state-of-the-art
baselines. The source code is publicly available at
https://github.com/hujunxianligong/CAPGNN.
