The Kleinberg HITS and the Google PageRank algorithms are eigenvector methods for identifying “authoritative” or “influential” articles, given hyperlink or citation information. That such algorithms should give reliable or consistent answers is surely a desideratum, and in [10], we analyzed when they can be expected to give stable rankings under small perturbations to the linkage patterns. In this paper, we extend the analysis and show how it gives insight into ways of designing stable link analysis methods. This in turn motivates two new algorithms, whose performance we study empirically using citation data and web hyperlink data.