A Dynamical System for PageRank with Time-Dependent Teleportation

TL;DR

This paper introduces a dynamical system model for PageRank that incorporates time-dependent teleportation, capturing how node importance changes with external interest over time, and demonstrates its utility on real-world networks.

Contribution

It develops a novel dynamical system for PageRank with time-varying teleportation, providing closed-form solutions and practical evaluation methods for dynamic network analysis.

Findings

Dynamic PageRank captures importance changes over time.

The model improves prediction tasks on real-world data.

External interest influences PageRank scores significantly.

Abstract

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.