Evolution of page popularity under random web graph models

The link structure of the Web can be viewed as a massive graph. The preferential attachment model and its variants are well-known random graph models that help explain the evolution of the web graph. However, those models assign more links to older pages without reference to the quality of web pages, which does not capture the real-world evolution of the web graph and renders the models inappropriate for studying the popularity evolution of new pages.We extend the preferential attachment model with page quality, where the probability of a page getting new links depends not only on its current degree but also on its quality. We study the distribution of degrees among different quality values, and prove that under discrete quality distributions, the degree sequence still follows a power law distribution. Then we use the model to study the evolution of page popularity. We show that for pages with the same quality, the older pages are more popular; if a younger page is better than an older page, then eventually the younger-and-better page will become more popular. We also use the model to study a randomized ranking scheme proposed earlier [18] and show that it accelerates popularity evolution of new pages.