  We propose a dynamical system that captures changes to the network centrality
of nodes as external interest in those nodes vary. We derive this system by
adding time-dependent teleportation to the PageRank score. The result is not a
single set of importance scores, but rather a time-dependent set. These can be
converted into ranked lists in a variety of ways, for instance, by taking the
largest change in the importance score. For an interesting class of the dynamic
teleportation functions, we derive closed form solutions for the dynamic
PageRank vector. The magnitude of the deviation from a static PageRank vector
is given by a PageRank problem with complex-valued teleportation parameters.
Moreover, these dynamical systems are easy to evaluate. We demonstrate the
utility of dynamic teleportation on both the article graph of Wikipedia, where
the external interest information is given by the number of hourly visitors to
each page, and the Twitter social network, where external interest is the
number of tweets per month. For these problems, we show that using information
from the dynamical system helps improve a prediction task and identify trends
in the data.
