2021/01/27 by Ming Li, Run-Ran Liu, Linyuan Lü +3 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Complex network #Continuum percolation theory #Network science #Network theory #Node (physics) #Opinion Dynamics and Social Influence #Pairwise comparison #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Percolation threshold #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1016/j.physrep.2020.12.003
published as Physics Reports 907, 1-68 (2021) · 88 pages,19 figures, 5 tables
openalex publication_date 2021/01/27 · crossref created 2021/01/27 · arxiv created 2021/01/28 · openalex created_date 2021/02/01 · crossref issued 2021/04/01 · crossref published 2021/04/01 · crossref published-print 2021/04/01 · arxiv updated 2021/04/20 · crossref deposited 2025/10/07 · crossref indexed 2026/08/05 · openalex updated_date 2026/08/05
In the last two decades, network science has blossomed and influenced various fields, such as statistical physics, computer science, biology and sociology, from the perspective of the heterogeneous interaction patterns of components composing the complex systems. As a paradigm for random and semi-random connectivity, percolation model plays a key role in the development of network science and its applications. On the one hand, the concepts and analytical methods, such as the emergence of the giant cluster, the finite-size scaling, and the mean-field method, which are intimately related to the percolation theory, are employed to quantify and solve some core problems of networks. On the other hand, the insights into the percolation theory also facilitate the understanding of networked systems, such as robustness, epidemic spreading, vital node identification, and community detection. Meanwhile, network science also brings some new issues to the percolation theory itself, such as percolation of strong heterogeneous systems, topological transition of networks beyond pairwise interactions, and emergence of a giant cluster with mutual connections. So far, the percolation theory has already percolated into the researches of structure analysis and dynamic modeling in network science. Understanding the percolation theory should help the study of many fields in network science, including the still opening questions in the frontiers of networks, such as networks beyond pairwise interactions, temporal networks, and network of networks. The intention of this paper is to offer an overview of these applications, as well as the basic theory of percolation transition on network systems.