2016/12/31 by Naoki Masuda, Mason A. Porter, Renaud Lambiotte · 1 citation
Physics and Astronomy · Computer Science · #physics.soc-ph #cond-mat.dis-nn #cs.SI
paper · pdf · doi:10.1016/j.physrep.2017.07.007
published as Physics Reports, 716-717, 1-58 (2017) · 12 figures, 2 tables; [v3] reflects the corrections we made in the two corrigenda (Physics Reports, 745, 96 (2018) and ibid., 851, 37-39 (2020))
arxiv created 2020/04/09 · arxiv updated 2020/04/13
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.