Network Properties Revealed through Matrix Functions

The newly emerging field of Network Science deals with the tasks of modelling, comparing and summarizing large data sets that describe complex interactions. Because pairwise affinity data can be stored in a twodimensional array, graph theory and applied linear algebra provide extremely useful tools. Here, we focus on the general concepts of centrality, communicability and betweenness, each of which quantifies important features in a network. Some recent work in the mathematical physics literature has shown that the exponential of a network's adjacency matrix can be used as the basis for defining and computing specific versions of these measures. We introduce here a general class of measures based on matrix functions, and show that a particular case involving a matrix resolvent arises naturally from graph-theoretic arguments. We also point out connections between these measures and the quantities typically computed when spectral methods are used for data mining tasks such as clust...

• Type: Journal
• Year: 2010
• Where: SIAMREV
• Authors: Ernesto Estrada, Desmond J. Higham
• Keywords: Data Mining Tasks, Matrix, Network Science Deals, SIAMREV 2010