Matrix Functions and Network Communicability Measures

Abstract In recent years, functions of matrices have played an increasingly important role in the analysis of graphs and networks, especially in the definition of powerful centrality and communicability measures and in the analysis of diffusion processes, both local and nonlocal. These techniques are having a significant impact in a variety of applications, ranging from social network analysis to chemical physics to the neurosciences. This contribution provides a succinct overview of how matrix functions can be used in the analysis of communicability in complex networks.