Analysis of node2vec random walks on networks. (25th November 2020)

• Record Type: Journal Article
• Authors: Meng, Lingqi; Masuda, Naoki
• Is Part Of: Proceedings. Volume 476:Number 2243(2020)
• Publication Date: 2020-11-25
• Subjects: diffusion -- relaxation time -- coalescence time -- second-order Markov chain -- community structure -- ring network; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2020.0447
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : 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 performance of the node2vec algorithm in these applications is considered to depend on properties of random walks that the algorithm uses. In the present study, we theoretically and numerically analyse random walks used by the node2vec. Those random walks are second-order Markov chains. We exploit the mapping of its transition rule to a transition probability matrix among directed edges to analyse the stationary probability, relaxation times in terms of the spectral gap of the transition probability matrix, and coalescence time. In particular, we show that node2vec random walk accelerates diffusion when walkers are designed to avoid both backtracking and visiting a neighbour of the previously visited node but do not avoid them completely.