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Representing nodes in a network as dense vectors node embeddings is importantfor understanding a given network and solving many downstream tasks. Inparticular, for weighted homophilous graphs where similar nodes are connectedwith larger edge weights, we desire node embeddings where node pairs withstrong weights have closer embeddings. Although random walk based nodeembedding methods like node2vec and node2vec+ do work for weighted networks viaincluding edge weights in the walk transition probabilities, our experimentsshow that the embedding result does not adequately reflect edge weights. Inthis paper, we propose ARGEW (Augmentation of Random walks by Graph EdgeWeights), a novel augmentation method for random walks that expands the corpusin such a way that nodes with larger edge weights end up with closerembeddings. ARGEW can work with any random walk based node embedding method,because it is independent of the random sampling strategy itself and works ontop of the already-performed walks. With several real-world networks, wedemonstrate that with ARGEW, compared to not using it, the desired pattern thatnode pairs with larger edge weights have closer embeddings is much clearer. Wealso examine ARGEW's performance in node classification: node2vec with ARGEWoutperforms pure node2vec and is not sensitive to hyperparameters (i.e.consistently good). In fact, it achieves similarly good results as supervisedGCN, even without any node feature or label information during training.Finally, we explain why ARGEW works consistently well by exploring thecoappearance distributions using a synthetic graph with clear structural roles.

Node Embedding for Homophilous Graphs with ARGEW: Augmentation of Random walks by Graph Edge Weights