  Graphs are ubiquitous due to their flexibility in representing social and
technological systems as networks of interacting elements. Graph representation
learning methods, such as node embeddings, are powerful approaches to map nodes
into a latent vector space, allowing their use for various graph tasks. Despite
their success, only few studies have focused on explaining node embeddings
locally. Moreover, global explanations of node embeddings remain unexplored,
limiting interpretability and debugging potentials. We address this gap by
developing human-understandable explanations for dimensions in node embeddings.
Towards that, we first develop new metrics that measure the global
interpretability of embedding vectors based on the marginal contribution of the
embedding dimensions to predicting graph structure. We say that an embedding
dimension is more interpretable if it can faithfully map to an understandable
sub-structure in the input graph - like community structure. Having observed
that standard node embeddings have low interpretability, we then introduce DINE
(Dimension-based Interpretable Node Embedding), a novel approach that can
retrofit existing node embeddings by making them more interpretable without
sacrificing their task performance. We conduct extensive experiments on
synthetic and real-world graphs and show that we can simultaneously learn
highly interpretable node embeddings with effective performance in link
prediction.
