Message passing methods on complex networks

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 perspective 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.

Automated summary

Networks and network computations have become essential for analyzing complex systems. Message passing methods, which involve the propagation of information between network nodes, are commonly used for calculating quantities on nodes. This perspective article discusses the application of message passing methods, provides examples and applications, and explores the connection between message passing and phase transitions in networks. It also discusses the limitations of message passing methods and describes recent methods that address these limitations.