A note on the PageRank of undirected graphs

@article{Grolmusz2015ANO,
  title={A note on the PageRank of undirected graphs},
  author={Vince Grolmusz},
  journal={Inf. Process. Lett.},
  year={2015},
  volume={115},
  pages={633-634}
}
  • V. Grolmusz
  • Published 9 May 2012
  • Mathematics
  • Inf. Process. Lett.
View PDF on arXiv
58 Citations
Highly Influential Citations
2
Background Citations
23
Methods Citations
11
Results Citations
3

58 Citations

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References

SHOWING 1-10 OF 15 REFERENCES

Local Graph Partitioning using PageRank Vectors

TLDR
An improved algorithm for computing approximate PageRank vectors, which allows us to find a cut with conductance at most oslash and approximately optimal balance in time O(m log4 m/oslash) in time proportional to its size.

A recommender system based on local random walks and spectral methods

TLDR
This paper designs recommender systems for weblogs based on the link structure among them and designs a similarity metric among nodes of a social network using the eigenvalues and eigenvectors of a normalized adjacency matrix of the social network graph.

The PageRank Citation Ranking : Bringing Order to the Web

TLDR
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.

Random Walks on Graphs: a Survey

Dedicated to the marvelous random walk of Paul Erd} os through universities, c ontinents, and mathematics Various aspects of the theory of random walks on graphs are surveyed. In particular,…

Spectral centrality measures in complex networks.

  • N. PerraS. Fortunato
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
TLDR
This work reviews and compares centrality measures based on spectral properties of graph matrices, and shall focus on PageRank, eigenvector centrality (EV), and the hub and authority scores of the HITS algorithm.

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TLDR
A novel method applicable in networks with directed edges (such as metabolic networks) that compensates for the low degree (non-hub) vertices in the network, and identifies important nodes, regardless of their hub properties is shown.

Fast Distributed PageRank Computation

Keyword Extraction Based on PageRank

TLDR
A keyword extraction algorithm based on WordNet and PageRank that applies UW-PageRank in the rough graph to do word sense disambiguation, prune the graph, and finally apply UW- PageRank again on the pruned graph to extract keywords.

The Anatomy of a Large-Scale Hypertextual Web Search Engine

Random Walks on Graphs: A Survey

TLDR
Estimates on the important parameters of access time, commute time, cover time and mixing time are discussed and recent algorithmic applications of random walks are sketched, in particular to the problem of sampling.