Recent advances of percolation theory in complex networks

TL;DR

This paper reviews recent developments in percolation theory within complex networks, highlighting various phase transition types, critical phenomena, and open questions in the field.

Contribution

It provides a concise overview of new theoretical advances in percolation transitions, including diverse transition types and their implications in complex systems.

Findings

Percolation transitions in complex networks can be discontinuous, hybrid, or infinite-order.

Recent theories include critical phenomena and finite-size scaling.

Open questions involve universal behaviors and applications.

Abstract

During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous transitions, the percolation transitions occurring in complex systems are often of different types such as discontinuous, hybrid, and infinite-order phase transitions. Thus, percolation has received considerable attention in network science community. Here we present a very brief review of percolation theory recently developed, which includes those types of phase transitions, critical phenomena, and finite-size scaling theory. Moreover, we discuss potential applications of theoretical results and several open questions including universal behaviors.