Message passing methods on complex networks

TL;DR

This review discusses message passing techniques for network analysis, illustrating their applications, limitations, and connections to phase transitions in complex systems.

Contribution

It provides a comprehensive overview of message passing methods, their applications, limitations, and recent advancements in analyzing complex networks.

Findings

Message passing methods effectively compute node quantities in complex networks.

Connections between message passing and phase transitions are explored.

Recent methods address limitations of traditional message passing approaches.

Abstract

Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A common task in network analysis is the calculation of quantities that reside on the nodes of a network, such as centrality measures, probabilities, or model states. In this review article we discuss message passing methods, a family of techniques for performing such calculations, based on the propagation of information between the nodes of a network. We introduce the message passing approach with a series of examples, give some illustrative applications and results, and discuss the deep connections between message passing and phase transitions in networks. We also point out some limitations of the message passing approach and describe some recently-introduced methods that address these limitations.