PageRank beyond the Web

  title={PageRank beyond the Web},
  author={David F. Gleich},
  • D. Gleich
  • Published 18 July 2014
  • Computer Science
  • ArXiv
Google's PageRank method was developed to evaluate the importance of web-pages via their link structure. The mathematics of PageRank, however, are entirely general and apply to any graph or network in any domain. Thus, PageRank is now regularly used in bibliometrics, social and information network analysis, and for link prediction and recommendation. It's even used for systems analysis of road networks, as well as biology, chemistry, neuroscience, and physics. We'll see the mathematics and… 

Figures from this paper

Importance of intrinsic and non-network contribution in PageRank centrality and its effect on PageRank localization

It is shown that PageRank value of a vertex also depends on its intrinsic, non-network contribution, and that localization of PageRank centrality depends upon the same intrinsic,non- network contribution.

A Study of PageRank in Undirected Graphs

This paper studies the PageRank sequence for undirected graphs of order six by PR vector, and provides an ordering for graphs by variance of PR vector which it’s variation is proportional with variance of degree sequence.

Ranking Users in Social Networks With Higher-Order Structures

This paper proposes a novel framework, motif-based PageRank (MPR), to incorporate higher-order structures into conventional PageRank computation, and conducts extensive experiments in three real-world networks to show that MPR can significantly improve the effectiveness of PageRank for ranking users in social networks.

Distributed Randomized Algorithms for PageRank Based on a Novel Interpretation

Gossip-type randomization is employed in the update schemes, and it is shown that the page selection need not be limited to the uniform distribution.

Strong Localization in Personalized PageRank Vectors

An upper-bound on the number of entries necessary to approximate a personalized PageRank vector in graphs with skewed degree sequences is derived and shows localization under mild assumptions on the maximum and minimum degrees.

Edinburgh Research Explorer Non-backtracking PageRank

A variation of PageRank that uses a non-backtracking random walk is considered, deriving an explicit representation of the new algorithm that can exploit structure and sparsity in the underlying network.

Boosting PageRank Scores by Optimizing Internal Link Structure

A heuristic-based algorithm that achieves 100 times improvements of the minimum PageRank score among selected 100 vertices by adding only dozens of edges is proposed.

Fatigued PageRank

This work formalize and exemplify the computation of Fatigued PageRank, evaluating it as a node ranking metric, as well as query-independent evidence in ad hoc document retrieval.

Neighborhood and PageRank methods for pairwise link prediction

A new link prediction task called “pairwise link prediction” is proposed that directly targets the prediction of new triangles, where one is tasked with finding which nodes are most likely to form a triangle with a given edge.

PageRank Computation via Web Aggregation in Distributed Randomized Algorithms

  • Atsushi SuzukiH. Ishii
  • Computer Science, Mathematics
    2019 IEEE 58th Conference on Decision and Control (CDC)
  • 2019
This paper presents extensions of the distributed algorithms which were recently proposed for the computation of PageRank that are modified for aggregation-based computation by grouping pages in the same domain.



PageRank for bibliographic networks

Several modifications of the classical PageRank formula adapted for bibliographic networks take into account not only the citation but also the co-authorship graph and turn out to be “better” than the standard PageRank ranking.

The PageRank Citation Ranking : Bringing Order to the Web

This paper describes PageRank, a mathod for rating Web pages objectively and mechanically, effectively measuring the human interest and attention devoted to them, and shows how to efficiently compute PageRank for large numbers of pages.

Exploiting the Block Structure of the Web for Computing

This work shows how to exploit the nested block structure of the web link graph to speed up the computation of PageRank by a 3-stage algorithm, and develops a variant of this algorithm that efficiently computes many different ``personalized'' PageRanks, and a variant that efficiently recomputes PageRank after node updates.

A Survey on PageRank Computing

  • P. Berkhin
  • Computer Science, Mathematics
    Internet Math.
  • 2005
The theoretical foundations of the PageRank formulation are examined, the acceleration of PageRank computing, in the effects of particular aspects of web graph structure on the optimal organization of computations, and in PageRank stability.

A Theoretical Analysis of Google's PageRank

This work starts from the definition of an intuitive formula that can be used to order the Web pages according to their importance, showing the need of a modification of this formula on a mathematical basis, and proves the substantial equivalence between this PageRank formula and the classic formula proposed in [3].

Modifications of Kleinberg's HITS algorithm using matrix exponentiation and web log records

Two modifications to the adjacency matrix input to the HITS algorithm are presented, which weights links according to how often they were followed by users in a given time period and incorporates user feedback without requiring direct user querying.

PageRank of integers

The PageRank vector of this matrix is computed numerically and it is shown that its probability is approximately inversely proportional to the PageRank index thus being similar to the Zipf law and the dependence established for the World Wide Web.

Local approximation of PageRank and reverse PageRank

It is proved that local approximation of PageRank is feasible if and only if the graph has low in-degree and admits fast PageRank convergence, and it is shown that reverse natural graphs tend to have low indegree while maintaining fastPageRank convergence.

Weighted PageRank algorithm

  • W. XingA. Ghorbani
  • Computer Science
    Proceedings. Second Annual Conference on Communication Networks and Services Research, 2004.
  • 2004
The weighted PageRank algorithms (WPR), an extension to the standard PageRank algorithm, is introduced, which takes into account the importance of both the inlinks and the outlinks of the pages and distributes rank scores based on the popularity of thepages.