This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternative...

We introduce Entropy Rank and Free Energy Rank, two methods to classify pages of the Web according to interest. These variants of PageRank are based on Ruelle’s thermodynamic formalism. They exhibit features from both PageRank and HITS methods.

In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding k new links. We consider the case that the new links must point to the given target node (backlinks). Previous work shows that this problem has no fully polynomial time approximation schemes unless P = NP . We present a polynomial time algorithm yielding a PageRank value within a constant...

We consider a variant of the contact process concerning multi-commodity allocation on networks. In this process, the demands for several types of commodities are initially given at some specified vertices and then the demands spread interactively on a contact graph. To allocate supplies in such a dynamic setting, we use a modified version of PageRank vectors, called Kronecker PageRank, to ident...

Topical PageRank (TPR) uses latent topic distribution inferred by Latent Dirichlet Allocation (LDA) to perform ranking of noun phrases extracted from documents. The ranking procedure consists of running PageRank K times, where K is the number of topics used in the LDA model. In this paper, we propose a modification of TPR, called Salience Rank. Salience Rank only needs to run PageRank once and ...

The importance of nodes in a network constantly fluctuates based on changes in the network structure as well as changes in external interest. We propose an evolving teleportation adaptation of the PageRank method to capture how changes in external interest influence the importance of a node. This framework seamlessly generalizes PageRank because the importance of a node will converge to the Pag...

In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding k new links. We consider the case that the new links must point to the given target node (backlinks). Previous work [7] shows that this problem has no fully polynomial time approximation schemes unless P = NP . We present a polynomial time algorithm yielding a PageRank value within a cons...

In a former paper [13] the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we introduce a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the...

We consider the web hyperlink matrix used by Google for computing the PageRank whose form is given by A(c) = [cP + (1 − c)E]T , where P is a row stochastic matrix, E is a row stochastic rank one matrix, and c ∈ [0, 1]. We determine the analytic expression of the Jordan form of A(c) and, in particular, a rational formula for the PageRank in terms of c. The use of extrapolation procedures is very...

The stability of Web link-based ranking algorithms was examined in recent works. Among the aspects investigated were the notions of rank stable algorithms and rank similar algorithms. Of special interest are stability results on a particular class of graphs, called authority connected graphs. This report considers three link-based ranking algorithms: PageRank, HITS and SALSA. We extend previous...