An Overview of Walk-Based Centrality and Communicability Measures for Network Analysis
After a general introduction to networks, I will review centrality and communicability measures for graphs based on walks. These measures are expressed in terms of functions of the adjacency matrix of the graph, such as the matrix exponential and the resolvent. I will review the notion of “total communicability” of a network and illustrate how this provides a measure of the connectivity of the underlying graph. Examples of applications to real-world networks from a variety of applications will be discussed.
The talk is addressed to a general audience and should be largely accessible to undergraduate students.