Graph convolutional network (GCN) nowadays become new state-of-the-art for networks representation learning. Most of the existing methods are single-granular methods that failed to analyze the graph at multi-granular views so as to lose abundant information. Advanced graph pooling techniques can be successfully benefiting from semi-supervised networks representation learning. How to capture multi-granular information through the graph pooling techniques on graphs without additional input features is a great challenge. Technically speaking, we propose our graph node embeddings framework, MGPOOL. First, inspired by the triadic influence learning, we use the 3-clique algorithm to coarsen the graph repeatedly. Three nodes of a triangle form a supernode. We treat the supernodes as key nodes for our graph pooling operations. That keeps the local relationship. These graphs capture consecutive 3-cliques from the finest to the coarsest to preserve global structural relationships. Second, we use the unsupervised single-granular algorithms on the coarsest graph to acquire its node embeddings. Based on that, our graph pooling operations combining with that node embeddings to generate another same size of the coarsest graph. This makes up for the uniqueness of the coarsening result at a time and expands the receptive field for each node to avoid high-proximity information lost. Third, we take the embeddings, the coarsest graph and new coarsest graph as uniform input of MGPOOL. We restore the coarsest graph to the original graph to get the original graph node embeddings. The experimental results on four public datasets, Wiki, Cora, CiteSeer, and DBLP, demonstrate that our method has a better Macro F1 value for node classification tasks and AUC and Ap value for link prediction than the baseline methods.

如今，图卷积网络（GCN）成为网络表示学习的最新技术。现有的大多数方法都是单粒度方法，无法在多粒度视图下分析图形，从而丢失大量信息。先进的图形池技术可以从半监督网络表示学习中成功受益。如何通过图上的图池化技术来捕获多粒度信息而没有其他输入功能，这是一个巨大的挑战。从技术上讲，我们提出了图节点嵌入框架MGPOOL。首先，受三重影响学习的启发，我们使用3-clique算法对图进行反复粗化。三角形的三个节点构成一个超节点。我们将超节点视为图池操作的关键节点。这样可以保持本地关系。这些图捕获了从最细到最粗的连续3-clique，以保留全局结构关系。其次，我们在最粗糙的图上使用无监督的单颗粒算法来获取其节点嵌入。基于此，我们的图池操作与该节点嵌入相结合，以生成另一个相同大小的最粗图。这一次弥补了粗化结果的唯一性，并扩展了每个节点的接收域，以避免丢失高邻近度信息。第三，我们将嵌入，最粗糙的图和新的最粗糙的图作为MGPOOL的统一输入。我们将最粗糙的图还原到原始图，以获得原始图节点嵌入。在四个公共数据集Wiki，Cora，CiteSeer和DBLP上的实验结果，