  Several state-of-the-art neural graph embedding methods are based on short
random walks (stochastic processes) because of their ease of computation,
simplicity in capturing complex local graph properties, scalability, and
interpretibility. In this work, we are interested in studying how much a
probabilistic bias in this stochastic process affects the quality of the nodes
picked by the process. In particular, our biased walk, with a certain
probability, favors movement towards nodes whose neighborhoods bear a
structural resemblance to the current node's neighborhood. We succinctly
capture this neighborhood as a probability measure based on the spectrum of the
node's neighborhood subgraph represented as a normalized laplacian matrix. We
propose the use of a paragraph vector model with a novel Wasserstein
regularization term. We empirically evaluate our approach against several
state-of-the-art node embedding techniques on a wide variety of real-world
datasets and demonstrate that our proposed method significantly improves upon
existing methods on both link prediction and node classification tasks.
