I will describe a new algorithm for summarizing properties of evolving networks. This type of data, recording connections that come and go over time, is being generated in many modern applications, including telecommunications and on-line human social behavior. The algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. The conventional approach of downweighting for length (messages become cor-rupted as they are passed along) is combined with the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used centrality measures that have proved popular in static network science to the case of dynamic net-works sampled at non-uniform points in time. In particular, indices can be computed that summarize the current ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by times arrow is captured naturally through the non-commutativity of matrix-matrix multiplication. I will give illustrative examples on both synthetic and real-world com-munication data sets. This talk covers joint work with Ernesto Estrada, Peter Grindrod and Mark Parsons.
Dept. of Mathematics and Statistics University of Strathclyde, Scotnald, UK