Abstract
In this paper a novel notion of Bipartite PageRank is introduced and limits of authority flow in bipartite graphs are investigated. As a starting point we simplify the proof of a theorem on personalized random walk in unimodal graphs that is fundamental to graph nodes clustering. As a consequence we generalize this theorem to bipartite graphs.
This is an extended version of the paper presented at the AI2012 Conference, Sept. 20th, 2012, Warsaw, Poland.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
An unoriented graph may serve as the representation of relationships spanned by a network of friends, telecommunication infrastructure or street network of a city, etc.
- 2.
For some versions of PageRank, like TrustRank \(p_{i,j}\) would differ from \(\frac{1}{outdeg(j)}\) giving preferences to some outgoing links over others. We are not interested in such considerations here.
- 3.
Called also principal eigenvector.
References
Bauckhage C (2008) Image tagging using pagerank over bipartite graphs. In: Proceedings of the 30th DAGM symposium on pattern recognition, pp 426–435. Springer, Berlin, Heidelberg. doi:10.1007/978-3-540-69321-5_43
Berkhin P (2005) A survey on PageRank computing. Internet Math 2:73–120
Chung F (2011) Pagerank as a discrete Green’s function. In: Ji L (ed) Geometry and analysis, I, Advanced lectures in mathematics (ALM), vol 17, pp 285–302. International Press of Boston, Boston
Deng H, Lyu MR, King I (2009) A generalized co-hits algorithm and its application to bipartite graphs. In: Proceedings of the 15th ACM SIGKDD international conference on knowledge discovery and data mining, KDD’09, pp 239–248. ACM, New York, NY, USA, Paris, June 28–July 1 2009 doi:10.1145/1557019.1557051
Frahm K, Georgeot B, Shepelyansky D (2011) Universal emergence of PageRank. J Phys A Math Theor 44:465101. doi:10.1088/1751-8113/44/46/465101
Garcia E, Pedroche F, Romance M (2013) On the localization of the personalized PageRank of complex networks. Linear Algebra Appl 439:640–652
Langville AN (2005) An annotated bibliography of papers about Markov chains and information retrieval. http://www.cofc.edu/langvillea/bibtexpractice.pdf
Langville AN, Meyer CD (2006) Google’s PageRank and beyond: the science of search engine rankings. Princeton University Press, Princeton
Link S (2011) Eigenvalue-based bipartite ranking. Bachelorarbeit/bachelor thesis. http://www.pms.ifi.lmu.de/publikationen/#PA_Stephan.Link
Meghabghab G, Kandel A (2008) Search engines, link analysis, and user’s web behavior. A unifying web mining approach, Studies in computational intelligence, vol 99. Springer, New York
Page L, Brin S, Motwani R, Winograd T (1999) The PageRank citation ranking: bringing order to the web. Technical Report 1999–66, Stanford InfoLab. http://ilpubs.stanford.edu:8090/422/
Zachary W (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33:452–473
Acknowledgments
This research has been supported by the Polish State budget scientific research funds.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kłopotek, M.A., Wierzchoń, S.T., Kłopotek, R.A., Kłopotek, E.A. (2016). Network Capacity Bound for Personalized Bipartite PageRank. In: Matwin, S., Mielniczuk, J. (eds) Challenges in Computational Statistics and Data Mining. Studies in Computational Intelligence, vol 605. Springer, Cham. https://doi.org/10.1007/978-3-319-18781-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-18781-5_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18780-8
Online ISBN: 978-3-319-18781-5
eBook Packages: EngineeringEngineering (R0)