Damping Effect on PageRank Distribution

TL;DR

This paper investigates how different damping schemes in PageRank models affect the distribution across various real-world networks, revealing that model variety enhances differentiation of network activities.

Contribution

It introduces a family of PageRank models with varied damping mechanisms, analyzes their responses, and provides an efficient algorithm for simultaneous computation on large graphs.

Findings

Response patterns vary less across models than across graphs.

Model variety helps differentiate network activities.

Spectral space for PageRank vectors is low-dimensional.

Abstract

This work extends the personalized PageRank model invented by Brin and Page to a family of PageRank models with various damping schemes. The goal with increased model variety is to capture or recognize a larger number of types of network activities, phenomena and propagation patterns. The response in PageRank distribution to variation in damping mechanism is then characterized analytically, and further estimated quantitatively on 6 large real-world link graphs. The study leads to new observation and empirical findings. It is found that the difference in the pattern of PageRank vector responding to parameter variation by each model among the 6 graphs is relatively smaller than the difference among 3 particular models used in the study on each of the graphs. This suggests the utility of model variety for differentiating network activities and propagation patterns. The quantitative analysis of the damping mechanisms over multiple damping models and parameters is facilitated by a highly efficient algorithm, which calculates all PageRank vectors at once via a commonly shared, spectrally invariant subspace. The spectral space is found to be of low dimension for each of the real-world graphs.