Node2vec random walks on graphs admit Markovian lifts to edge and wedge spaces that guarantee ergodicity and recurrence under mild conditions, with regularity equivalent to a weighted Eulerianity condition.
Analysis of node2vec random walks on networks
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node2vec or triangle-biased random walks: stationarity, regularity & recurrence
Node2vec random walks on graphs admit Markovian lifts to edge and wedge spaces that guarantee ergodicity and recurrence under mild conditions, with regularity equivalent to a weighted Eulerianity condition.