Abstract
We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent. The difference between these two power laws is in a multiplicative constant, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and the damping factor. The out-degree distribution has a minor effect, which we explicitly quantify. Finally, we propose a ranking scheme which does not depend on out-degrees.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gyongyi, Z., Garcia-Molina, H., Pedersen, J.: Combating Web spam with TrustRank. In: VLDB 2004: 30th International Conference on Very Large Data Bases, pp. 576–587 (2004)
Andersen, R., Chung, F., Lang, K.: Local graph partitioning using PageRank vectors. In: FOCS 2006: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 475–486 (2006)
Chen, P., Xie, H., Maslov, S., Redner, S.: Finding scientific gems with Google. Technical Report 0604130, arxiv/physics (2006)
Brin, S., Page, L.: The anatomy of a large-scale hypertextual Web search engine. Comput. Networks 33, 107–117 (1998)
Pandurangan, G., Raghavan, P., Upfal, E.: Using PageRank to characterize Web structure. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, Springer, Heidelberg (2002)
Donato, D., Laura, L., Leonardi, S., Millozi, S.: Large scale properties of the Web-graph. Eur. Phys. J. 38, 239–243 (2004)
Fortunato, S., Boguna, M., Flammini, A., Menczer, F.: How to make the top ten: Approximating PageRank from in-degree. Technical Report 0511016, arXiv/cs (2005)
Becchetti, L., Castillo, C.: The distribution of PageRank follows a power-law only for particular values of the damping factor. In: WWW 2006: Proceedings of the 15th International Conference on World Wide Web, pp. 941–942. ACM Press, New York (2006)
Avrachenkov, K., Lebedev, D.: PageRank of scale-free growing networks. Internet Math. 3(2), 207–231 (2006)
Fortunato, S., Flammini, A.: Random walks on directed networks: the case of PageRank. Technical Report 0604203, arXiv/physics (2006)
Albert, R., Barabási, A.L.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Litvak, N., Scheinhardt, W.R.W., Volkovich, Y.: In-degree and PageRank of Web pages: Why do they follow similar power laws? Memorandum 1807, University of Twente, Enschede (2006) (to appear in Internet Mathematics)
Eiron, N., McCurley, K.S., Tomlin, J.A.: Ranking the Web frontier. In: WWW 2004: Proceedings of the 13th International Conference on World Wide Web, pp. 309–318. ACM Press, New York (2004)
Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Statac, R., Tomkins, A., Wiener, J.: Graph structure in the Web. Comput. Networks 33, 309–320 (2000)
Capocci, A., Servedio, V.D.P., Colaiori, F., Buriol, L.S., Donato, D., Leonardiand, S., Caldarelli, G.: Preferential attachment in the growth of social networks: the case of Wikipedia. Technical Report 0602026, arXiv/physics (2006)
Langville, A.N., Meyer, C.D.: Deeper inside PageRank. Internet Math. 1, 335–380 (2003)
http://law.dsi.unimi.it/ (Accessed in January 2007)
Baeza-Yates, R., Castillo, C., Efthimiadis, E.: Characterization of national Web domains. ACM TOITÂ 7(2) (May 2007)
Newman, M.E.J.: Power laws, Pareto distributions and Zipf’s law. Cont. Phys. 46, 323–351 (2005)
Ross, S.M.: Stochastic processes, 2nd edn. John Wiley & Sons Inc., New York (1996)
Ross, S.M.: The inspection paradox. Probab. Engrg. Inform. Sci. 17, 47–51 (2003)
Avrachenkov, K., Litvak, N.: The effect of new links on Google PageRank. Stoch. Models 22(2), 319–331 (2006)
Aldous, D.J., Bandyopadhyay, A.: A survey of max-type recursive distributional equations. Ann. Appl. Probab. 15, 1047–1110 (2005)
Liu, Q.: Asymptotic properties and absolute continuity of laws stable by random weighted mean. Stochastic Process. Appl. 95(1), 83–107 (2001)
Jessen, A.H., Mikosch, T.: Regularly varying functions. Publications de l’institut mathematique, Nouvelle série 79(93) (2006)
Donato, D., Laura, L., Leonardi, S., Millozzi, S.: The Web as a graph: How far we are. ACM Trans. Inter. Tech. 7(1) (February 2007)
Kleinberg, J.M.: Authoritative sources in a hyperlinked environment. JACM 46(5), 604–632 (1999)
Lempel, R., Moran, S.: The stochastic approach for link-structure analysis (SALSA) and the TKC effect. Comput. Networks 33(1-6), 387–401 (2000)
Farahat, A., LoFaro, T., Miller, J.C., Rae, G., Ward, L.A.: Authority rankings from HITS, PageRank, and SALSA: Existence, uniqueness, and effect of initialization. SISC 27(4), 1181–1201 (2006)
Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge University Press, Cambridge (1989)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Volkovich, Y., Litvak, N., Donato, D. (2007). Determining Factors Behind the PageRank Log-Log Plot. In: Bonato, A., Chung, F.R.K. (eds) Algorithms and Models for the Web-Graph. WAW 2007. Lecture Notes in Computer Science, vol 4863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77004-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-77004-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77003-9
Online ISBN: 978-3-540-77004-6
eBook Packages: Computer ScienceComputer Science (R0)