Network Science is a rapidly growing interdisciplinary area
at the intersection of mathematics, computer science, and a
multitude of disciplines from the natural and life sciences
to the social sciences and even the humanities. Network
analysis methods are now widely used in proteomics, in the
study of social networks (both human and animal), in finance,
in ecology, in bibliometric studies, in archeology, and in a
host of other fields.

In this talk I will introduce the audience to some of the
mathematical and computational problems and methods of complex
networks, with an emphasis on the basic notions of centrality
and communicability. More specifically, I will describe some of
the problems in large-scale numerical linear algebra arising in
this area, and how they differ from the corresponding problems
encountered in more traditional applications of numerical analysis.

The talk will be accessible to students, requiring only a modest
background in linear algebra and graph theory.