Analysis of node2vec random walks on networks: Node2vec random walks on networks

Lingqi Meng, Naoki Masuda

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number0447
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume476
Issue number2243
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • coalescence time
  • community structure
  • diffusion
  • relaxation time
  • ring network
  • second-order Markov chain

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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