“node2vec random walks: the first few steps”
Venerdì 15 Maggio 2026, ore 15:00 - Aula 2AB40 - Gianmarco Bet (Università di Firenze)
Abstract
The node2vec random walk is a non-Markovian random walk on the vertex set of a graph defined in terms of three parameters which control the probability of, respectively, backtracking moves, moves within triangles, and moves to the remaining neighbouring nodes. Despite its widespread use in applications, little is known about it from a mathematical standpoint. In this talk, I will present the first results describing the long-time behaviour of this random walk. More specifically, I will give mild sufficient conditions on the underlying finite or infinite graph to guarantee ergodicity, reversibility, recurrence and a characterization of the invariant measure. One of the key findings is that if the underlying graph is regular, the invariant measure has a simple (and indeed neat) explicit expression.
Based on joint work with L. Avena, L. Schroeder and C. Stegehuis.
