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Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be used for tasks such as multi-label classification and link prediction. The usefulness of node2vec in these applications is considered to be contingent upon properties of random walks that the node2vec algorithm uses. In the present study, we theoretically and numerically analyze random walks used by the node2vec. The node2vec random walk is a second-order Markov chain. We exploit the mapping of its transition rule to a transition probability matrix among directed edges to analyze the stationary probability, relaxation times, and coalescence time. In particular, we provide a multitude of evidence that node2vec random walk accelerates diffusion when its parameters are tuned such that walkers avoid both back-tracking and visiting a neighbor of the previously visited node, but not excessively.
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an analytical ex
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical processes
Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously distributed. Here,
Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed to migrate
Node embedding is a powerful approach for representing the structural role of each node in a graph. $textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph. Ho