Message-passing approach for percolation on the networked system: A mini-review

¹ School of Computer Science and Technology, Zhejiang Normal University - Jinhua 321004, China
² Key Laboratory of Intelligent Education Technology and Application of Zhejiang Province, Zhejiang Normal University - Jinhua 321004, China
³ School of Cyber Science and Engineering, Shanghai Jiao Tong University - Shanghai 200240, China
⁴ School of Public Health, Chongqing Medical University - Chongqing, 400016, China

Received: 15 May 2024
Accepted: 18 June 2024

Abstract

Network percolation is one of the core topics in network science, especially in understanding and optimizing the robustness of real-world networks. As a powerful tool, the message-passing approach shows unique advantages in characterizing network percolation compared with the mean-field approach. This approach simulates the behavioural response when the network is damaged by transmitting and updating messages between network nodes, thereby accurately assessing the robustness of the network. This paper reviews the progress of message-passing approaches in network percolation on simple networks, multilayer networks and higher-order networks in recent years and discusses the application of this approach in other research fields. Finally, we discuss future research directions around this approach.