Graph Convolutional Networks (GCNs) have been widely applied in various
fields due to their significant power on processing graph-structured data.
Typical GCN and its variants work under a homophily assumption (i.e., nodes
with same class are prone to connect to each other), while ignoring the
heterophily which exists in many real-world networks (i.e., nodes with
different classes tend to form edges). Existing methods deal with heterophily
by mainly aggregating higher-order neighborhoods or combing the immediate
representations, which leads to noise and irrelevant information in the result.
But these methods did not change the propagation mechanism which works under
homophily assumption (that is a fundamental part of GCNs). This makes it
difficult to distinguish the representation of nodes from different classes. To
address this problem, in this paper we design a novel propagation mechanism,
which can automatically change the propagation and aggregation process
according to homophily or heterophily between node pairs. To adaptively learn
the propagation process, we introduce two measurements of homophily degree
between node pairs, which is learned based on topological and attribute
information, respectively. Then we incorporate the learnable homophily degree
into the graph convolution framework, which is trained in an end-to-end schema,
enabling it to go beyond the assumption of homophily. More importantly, we
theoretically prove that our model can constrain the similarity of
representations between nodes according to their homophily degree. Experiments
on seven real-world datasets demonstrate that this new approach outperforms the
state-of-the-art methods under heterophily or low homophily, and gains
competitive performance under homophily.

本文提出了一种新的传播机制，可以智能地根据同类和异类节点之间的同质性或异质性自动更改传播和聚合过程，并基于拓扑和属性信息学习同质性度量方法，以刻画不同类别节点之间的相似度，在七个现实世界数据集上实验表明该方法优于现有方法。

适应传播机制的强力图卷积网络，用于同构性和异构性

Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism  for Homophily and Heterophily

In this paper, we present a general framework to scale graph autoencoders
(AE) and graph variational autoencoders (VAE). This framework leverages graph
degeneracy concepts to train models only from a dense subset of nodes instead
of using the entire graph. Together with a simple yet effective propagation
mechanism, our approach significantly improves scalability and training speed
while preserving performance. We evaluate and discuss our method on several
variants of existing graph AE and VAE, providing the first application of these
models to large graphs with up to millions of nodes and edges. We achieve
empirically competitive results w.r.t. several popular scalable node embedding
methods, which emphasizes the relevance of pursuing further research towards
more scalable graph AE and VAE.

该论文提出了一个基于图退化概念的图自编码器和图变分自编码器的扩展框架，它可以训练只用稠密节点子集的模型而不是整个图。结合一个简单但有效的传播机制，方法可显著提高可扩展性和训练速度，并在多种现有图自编码器和图变分自编码器的变体上进行了评估和讨论。实验结果表明，该方法在大规模图上具有与其他流行的节点嵌入方法相当的性能。