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Graph vertex embeddings based on random walks have become increasinglyinfluential in recent years, showing good performance in several tasks as theyefficiently transform a graph into a more computationally digestible formatwhile preserving relevant information. However, the theoretical properties ofsuch algorithms, in particular the influence of hyperparameters and of thegraph structure on their convergence behaviour, have so far not beenwell-understood. In this work, we provide a theoretical analysis forrandom-walks based embeddings techniques. Firstly, we prove that, under someweak assumptions, vertex embeddings derived from random walks do indeedconverge both in the single limit of the number of random walks $N \to \infty$and in the double limit of both $N$ and the length of each random walk$L\to\infty$. Secondly, we derive concentration bounds quantifying the convergerate of the corpora for the single and double limits. Thirdly, we use theseresults to derive a heuristic for choosing the hyperparameters $N$ and $L$. Wevalidate and illustrate the practical importance of our findings with a rangeof numerical and visual experiments on several graphs drawn from real-worldapplications.

Delving Into Deep Walkers: A Convergence Analysis of Random-Walk-Based Vertex Embeddings