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The objective of unsupervised graph representation learning (GRL) is to learna low-dimensional space of node embeddings that reflect the structure of agiven unlabeled graph. Existing algorithms for this task rely on negativesampling objectives that maximize the similarity in node embeddings at nearbynodes (referred to as "cohesion") by maintaining positive and negative corpusof node pairs. While positive samples are drawn from node pairs that co-occurin short random walks, conventional approaches construct negative corpus byuniformly sampling random pairs, thus ignoring valuable information aboutstructural dissimilarity among distant node pairs (referred to as"separation"). In this paper, we present a novel Distance-aware NegativeSampling (DNS) which maximizes the separation of distant node-pairs whilemaximizing cohesion at nearby node-pairs by setting the negative samplingprobability proportional to the pair-wise shortest distances. Our approach canbe used in conjunction with any GRL algorithm and we demonstrate the efficacyof our approach over baseline negative sampling methods over downstream nodeclassification tasks on a number of benchmark datasets and GRL algorithms. Allour codes and datasets are available athttps://github.com/Distance-awareNS/DNS/.

Maximizing Cohesion and Separation in Graph Representation Learning: A Distance-aware Negative Sampling Approach