Representing nodes in a network as dense vectors node embeddings is important for understanding a given network and solving many downstream tasks. In particular, for weighted homophilous graphs where similar nodes are connected with larger edge weights, we desire node embeddings where node pairs with strong weights have closer embeddings. Although random walk based node embedding methods like node2vec and node2vec+ do work for weighted networks via including edge weights in the walk transition probabilities, our experiments show that the embedding result does not adequately reflect edge weights. In this paper, we propose ARGEW (Augmentation of Random walks by Graph Edge Weights), a novel augmentation method for random walks that expands the corpus in such a way that nodes with larger edge weights end up with closer embeddings. ARGEW can work with any random walk based node embedding method, because it is independent of the random sampling strategy itself and works on top of the already-performed walks. With several real-world networks, we demonstrate that with ARGEW, compared to not using it, the desired pattern that node pairs with larger edge weights have closer embeddings is much clearer. We also examine ARGEW's performance in node classification: node2vec with ARGEW outperforms pure node2vec and is not sensitive to hyperparameters (i.e. consistently good). In fact, it achieves similarly good results as supervised GCN, even without any node feature or label information during training. Finally, we explain why ARGEW works consistently well by exploring the coappearance distributions using a synthetic graph with clear structural roles.

在本文中，我们提出了一种新颖的增强型随机游走方法 ARGEW（Augmentation of Random Walks by Graph Edge Weights），该方法通过扩展语料库，在节点嵌入中使具有较大边权重的节点更接近，从而能够更好地反映边权重，并在节点分类中表现出良好的性能，在训练过程中无需节点特征或标签信息。

使用ARGEW对同质图进行节点嵌入:通过图边权重增强随机游走