The largest information networks studied display a number of characteristic properties including a highly-skewed and possibly power-law degree distribution as well as local clustering. We'll describe a few recent results on how these properties imply localization results for various graph diffusion operations when expressed as a function of a matrix. One of the best known examples is the heat kernel, where we'll show conditions when the heat-kernel of a graph remains localized, or effectively sparse, as the graph size grows.

David Gleich is an Assistant Professor at Purdue University. His research is in the area of high performance and large scale matrix computations and tends to focus on analyzing large data from information networks, social networks, protein networks, and scientific simulations. David received his Ph.D. in Computational and Mathematical Engineering from Stanford University in 2009 Prior to joining Purdue, David was the John von Neumann post-doctoral fellow at Sandia National Labs.