Stability and Similarity of Link Analysis Ranking Algorithms.

Recently, there has been a surge of research activity in the area of link analysis ranking, where hyperlink structures are used to determine the relative authority of webpages. One of the seminal works in this area is that of Kleinberg [Kleinberg 98], who proposed the HITS algorithm. In this paper, we undertake a theoretical analysis of the properties of the HITS algorithm on a broad class of random graphs. Working within the framework of Borodin et al. [Borodin et al. 05], we prove that, under some assumptions, on this class (a) the HITS algorithm is stable with high probability and (b) the HITS algorithm is similar to the InDegree heuristic that assigns to each node weight proportional to the number of incoming links. We demonstrate that our results go through for the case that the expected in-degrees of the graph follow a power law distribution. We also study experimentally the similarity between HITS and InDegree, and we investigate the general conditions under which the two algorithms are similar.