Understanding percolation phase transition behaviors in complex networks from the macro and meso-micro perspectives. (1st September 2022) - Dong, Gaogao; Sun, Zhipeng; Sun, Nannan; Wang, Fan
Abstract: Over the most recent twenty years, network science has bloomed and impacted different fields such as statistical physics, computer science, sociology, and so on. Studying the percolation behavior of a network system has a very important role in vital nodes identification, ranking, network resilience, and propagation behavior of networks. When a network system undergoes failures, network connectivity is broken. In this perspective, the percolation behavior of the giant connected component and finite-size connected components is explored in depth from the macroscopic and meso-microscopic views, respectively. From a macro perspective, a single network system always shows second-order phase transitions, but for a coupled network system, it shows rich percolation behaviors for various coupling strength, coupling patterns and coupling mechanisms. Although the giant component accounts for a large proportion in the real system, it cannot be neglected that when the network scale is large enough, the scale of finite-size connected components has an important influence on network connectivity. We here systematically analyze the phase transition behaviors of finite-size connected components that are different from the giant component from a meso-microscopic perspective. Studying percolation behaviors from the macro and meso-micro perspectives is helpful for a comprehensive understanding of many fields of network science, such as time-series networks, adaptive networks, and higher-order networks. The intention of this paper is to provide a frontier research progress and promising research direction of network percolation from the two perspectives, as well as the essential theory of percolation transitions on a network system.