Title: 'Variations on PageRank': Generalizing PageRank, multidamping and
inhomogeneous matrix products

Efstratios Gallopoulos
Computer Engineering & Informatics Department, University of Patras, Greece

Since its creation around 1998, PageRank has become a popular algorithm,
both for "math and money". We briefly review the method and then take
the math theme and present an approach, we call multidamping, that helps
to re-interpret some link-based functional rankings. Multidamping is
based on some interesting properties of "Google matrices". A key result
is that under certain conditions, matrix polynomials with argument the
normalized stochastic matrix used to construct the Google matrix can be
factorized as products of Google matrices with different damping factors.
We describe algorithms for computing the damping factors and apply them
on some published functional rankings such as Linear Rank, TotalRank
and HyperbolicRank. We then examine the spectral properties of general
inhomogeneous products of Google matrices, the convergence of such
products, and the implication of these results to the area of link-based
rankings.