Damping Effect on PageRank Distribution

We extend the personalized PageRank model invented by Brin and Page to a model family, endowing each model with a characteristic damping scheme. On social bio-physical networks of today, actions, reactions and counteractions vary or unfold more than ever. It is imperative to advance modeling methodology and enrich model repertoire in order to capture or uncover, differentiate and recognize various network phenomenons and propagation patterns. We investigate the response in PageRank distribution to inter- and intra-model variation in damping. Our investigation leads to new theoretical and empirical findings. In empirical study, we use quantitative measures to assess damping effect of 3 particular models on 6 large realworld link graphs. It is found that the patterns of PageRank vectors vary more distinctively among the 3 models on each graph than among the 6 graphs with each model. This suggests the utility of model variety for differentiating network activities and propagation patterns. Our quantitative analysis of damping effect, over many model and parameter changes, 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 with each of the real-world link graphs.