DeepWalk
DeepWalk
**DeepWalk** learns embeddings (social representations) of a graph's vertices, by modeling a stream of short random walks. Social representations are latent features of the vertices that capture neighborhood similarity and community membership. These latent representations encode social relations in a continuous vector space with a relatively small number of dimensions. It generalizes neural language models to process a special language composed of a set of randomly-generated walks. 

The goal is to learn a latent representation, not only a probability distribution of node co-occurrences, and so as to introduce a mapping function $\Phi \colon v \in V \mapsto \mathbb{R}^{|V|\times d}$.
This mapping $\Phi$ represents the latent social representation associated with each vertex $v$ in the graph. In practice, $\Phi$ is represented by a $|V| \times d$ matrix of free parameters.
DeepWalk: Online Learning of Social Representations
https://paperswithcode.com/paper/deepwalk-online-learning-of-social
DeepWalk: Online Learning of Social Representations