research-article

PageRank Beyond the Web

Author:

David F. GleichAuthors Info & Claims

SIAM Review, Volume 57, Issue 3

Pages 321 - 363

https://doi.org/10.1137/140976649

Published: 01 January 2015 Publication History

Abstract

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 ideas that unite these diverse applications.

References

[1]

B. Abrahao, S. Soundarajan, J. Hopcroft, and R. Kleinberg (2012), On the separability of structural classes of communities, in Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '12, ACM, New York, pp. 624--632.

[2]

D. Aldous and J. A. Fill (2002), Reversible Markov Chains and Random Walks on Graphs, unfinished monograph; recompiled 2014, available online from http://www.stat.berkeley.edu/ $\sim$aldous/RWG/book.html.

[3]

S. Allesina and M. Pascual (2009), Googling food webs: Can an eigenvector measure species' importance for coextinctions?, PLoS Comput. Biol., 5, e1000494.

[4]

R. Andersen, F. Chung, and K. Lang (2006), Local graph partitioning using PageRank vectors, in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, IEEE, pp. 475--486.

[5]

W. N. J. Anderson and T. D. Morley (1985), Eigenvalues of the Laplacian of a graph, Linear Multilinear Algebra, 18, pp. 141--145.

[6]

A. Arasu, J. Novak, A. Tomkins, and J. Tomlin (2002), PageRank computation and the structure of the web: Experiments and algorithms, in Proceedings of the 11th International Conference on the World Wide Web, Poster session. www2002.org/COROM/poster.173.pdf.

[7]

K. Avrachenkov, N. Litvak, and K. S. Pham (2007), Distribution of PageRank mass among principle components of the web, in Proceedings of the 5th Workshop on Algorithms and Models for the Web Graph (WAW2007), A. Bonato and F. C. Graham, eds., Lecture Notes in Comput. Sci. 4863, Springer, New York, pp. 16--28.

[8]

K. Avrachenkov, B. Ribeiro, and D. Towsley (2010), Improving random walk estimation accuracy with uniform restarts, in Algorithms and Models for the Web-Graph, R. Kumar and D. Sivakumar, eds., Lecture Notes in Comput. Sci. 6516, Springer, Berlin, Heidelberg, pp. 98--109.

[9]

L. Backstrom and J. Leskovec (2011), Supervised random walks: Predicting and recommending links in social networks, in Proceedings of the Fourth ACM International Conference on Web Search and Data Mining, WSDM '11, ACM, New York, pp. 635--644.

[10]

R. Baeza-Yates, P. Boldi, and C. Castillo (2006), Generalizing PageRank: Damping functions for link-based ranking algorithms, in Proceedings of the 29th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR2006), Seattle, WA, ACM, New York, pp. 308--315.

[11]

B. Bahmani, A. Chowdhury, and A. Goel (2010), Fast incremental and personalized PageRank, Proc. VLDB Endow., 4, pp. 173--184.

[12]

A. Balmin, V. Hristidis, and Y. Papakonstantinou (2004), ObjectRank: Authority-based keyword search in databases, in Proceedings of the Thirtieth International Conference on Very Large Data Bases, Volume 30, VLDB '04, VLDB Endowment, pp. 564--575.

[13]

Z. Bar-Yossef and L.-T. Mashiach (2008), Local approximation of PageRank and reverse PageRank, in CIKM '08: Proceedings of the 17th ACM conference on Information and Knowledge Management, ACM, New York, pp. 279--288.

[14]

D. S. Bassett and E. Bullmore (2006), Small-world brain networks, The Neuroscientist, 12, pp. 512--523.

[15]

M. Bayati, D. F. Gleich, A. Saberi, and Y. Wang (2013), Message-passing algorithms for sparse network alignment, ACM Trans. Knowl. Discov. Data, 7, pp. 3:1--3:31.

[16]

L. Becchetti, C. Castillo, D. Donato, R. Baeza-Yates, and S. Leonardi (2008), Link analysis for web spam detection, ACM Trans. Web, 2, pp. 1--42.

[17]

M. Benzi, E. Estrada, and C. Klymko (2013), Ranking hubs and authorities using matrix functions, Linear Algebra Appl., 438, pp. 2447--2474.

[18]

P. Berkhin (2005), A survey on PageRank computing, Internet Math., 2, pp. 73--120.

[19]

A. Berman and R. J. Plemmons (1994), Nonnegative Matrices in the Mathematical Sciences, Classics Appl. Math. 9, SIAM, Philadelphia.

[20]

M. Bianchini, M. Gori, and F. Scarselli (2005), Inside PageRank, ACM Trans. Internet Technologies, 5, pp. 92--128.

[21]

D. A. Bini, G. M. D. Corso, and F. Romani (2010), A combined approach for evaluating papers, authors and scientific journals, J. Comput. Appl. Math., 234, pp. 3104--3121.

[22]

D. M. Blei, A. Y. Ng, and M. I. Jordan (2003), Latent Dirichlet allocation, J. Mach. Learn. Res., 3, pp. 993--1022.

[23]

V. D. Blondel, A. Gajardo, M. Heymans, P. Senellart, and P. Van Dooren (2004), A measure of similarity between graph vertices: Applications to synonym extraction and web searching, SIAM Rev., 46, pp. 647--666.

[24]

P. Boldi (2005), TotalRank: Ranking without damping, in Poster Proceedings of the 14th International Conference on the World Wide Web (WWW2005), ACM Press, New York, pp. 898--899.

[25]

P. Boldi, F. Bonchi, C. Castillo, D. Donato, A. Gionis, and S. Vigna (2008), The query-flow graph: Model and applications, in Proceedings of the 17th ACM Conference on Information and Knowledge Management, CIKM '08, ACM, New York, pp. 609--618.

[26]

P. Boldi, F. Bonchi, C. Castillo, and S. Vigna (2009a), Voting in social networks, in Proceedings of the 18th ACM Conference on Information and Knowledge Management, CIKM '09, ACM, New York, pp. 777--786.

[27]

P. Boldi, F. Bonchi, C. Castillo, and S. Vigna (2011), Viscous democracy for social networks, Commun. ACM, 54, pp. 129--137.

[28]

P. Boldi, R. Posenato, M. Santini, and S. Vigna (2007), Traps and pitfalls of topic-biased PageRank, in Fourth International Workshop on Algorithms and Models for the Web-Graph, WAW2006, Lecture Notes in Comput. Sci., Springer-Verlag, New York, pp. 107--116.

[29]

P. Boldi, M. Santini, and S. Vigna (2005), PageRank as a function of the damping factor, in Proceedings of the 14th International Conference on the World Wide Web (WWW2005), Chiba, Japan, ACM Press, New York, pp. 557--566.

[30]

P. Boldi, M. Santini, and S. Vigna (2009b), PageRank: Functional dependencies, ACM Trans. Inf. Syst., 27, pp. 1--23.

[31]

J. Bollen, M. A. Rodriquez, and H. Van de Sompel (2006), Journal status, Scientometrics, 69, pp. 669--687.

[32]

S. Brin and L. Page (1998), The anatomy of a large-scale hypertextual web search engine, Comput. Netw. ISDN Syst., 30, pp. 107--117.

[33]

T. Callaghan, P. J. Mucha, and M. A. Porter (2007), Random walker ranking for NCAA division I-A football, Amer. Math. Monthly, 114, pp. 761--777.

[34]

P. Chen, H. Xie, S. Maslov, and S. Redner (2007), Finding scientific gems with Google's PageRank algorithm, J. Informetrics, 1, pp. 8--15.

[35]

A. Chepelianskii (2010), Towards Physical Laws for Software Architecture, arXiv preprint, cs.SE, 1003.5455.

[36]

F. Chung (2005), Laplacians and the Cheeger inequality for directed graphs, Ann. Comb., 9, pp. 1--19.

[37]

F. Chung (2007), The heat kernel as the PageRank of a graph, Proc. Natl. Acad. Sci. USA, 104, pp. 19735--19740.

[38]

F. Chung, A. Tsiatas, and W. Xu (2011), Dirichlet PageRank and trust-based ranking algorithms, in Algorithms and Models for the Web Graph, Lecture Notes in Comput. Sci. 6732, Springer, Berlin, Heidelberg, pp. 103--114.

[39]

F. R. L. Chung (1992), Spectral Graph Theory, AMS, Providence, RI.

[40]

W. N. Colley (2002), Colley's Bias Free College Football Ranking Method: The Colley Matrix Explained, Tech. Report, Princeton University, Princeton, NJ.

[41]

P. G. Constantine and D. F. Gleich (2010), Random alpha PageRank, Internet Math., 6, pp. 189--236.

[42]

J. J. Crofts and D. J. Higham (2011), Googling the brain: Discovering hierarchical and asymmetric network structures, with applications in neuroscience, Internet Math., 7, pp. 233--254.

[43]

M. Cutts (2006), Matt Cutts: Gadgets, Google, and SEO, Q&A thread, March 27, 2006. Available online from http://www.mattcutts.com/blog/q-a-thread-march-27-2006/.

[44]

M. Cutts (2009), PageRank sculpting, Matt Cutts: Gadgets, Google, and SEO blog. Available online from http://www.mattcutts.com/blog/pagerank-sculpting/.

[45]

T. A. Davis and Y. Hu (2011), The University of Florida sparse matrix collection, ACM Trans. Math. Softw., 38, pp. 1:1--1:25.

[46]

G. M. Del Corso, A. Gullí, and F. Romani (2005), Fast PageRank computation via a sparse linear system, Internet Math., 2, pp. 251--273.

[47]

I. S. Dhillon (2001), Co-clustering documents and words using bipartite spectral graph partitioning, in Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '01, ACM, New York, pp. 269--274.

[48]

Y. Du, J. Leung, and Y. Shi (2008), PerturbationRank: A Non-monotone Ranking Algorithm, Tech. Report, University of Michigan.

[49]

N. Eiron, K. S. McCurley, and J. A. Tomlin (2004), Ranking the web frontier, in Proceedings of the 13th International Conference on the World Wide Web (WWW2004), ACM, New York, pp. 309--318.

[50]

Y.-H. Eom, P. Aragón, D. Laniado, A. Kaltenbrunner, S. Vigna, and D. L. Shepelyansky (2014), Interactions of Cultures and Top People of Wikipedia from Ranking of 24 Language Editions, arXiv preprint, cs.SI, 1405.7183.

[51]

E. Estrada (2000), Characterization of 3D molecular structure, Chem. Phys. Lett., 319, pp. 713--718.

[52]

E. Estrada and D. J. Higham (2010), Network properties revealed through matrix functions, SIAM Rev., 52, pp. 696--714.

[53]

E. Estrada, D. J. Higham, and N. Hatano (2008), Communicability and multipartite structures in complex networks at negative absolute temperatures, Phys. Rev. E, 78, 026102.

[54]

A. Farahat, T. LoFaro, J. C. Miller, G. Rae, and L. A. Ward (2006), Authority rankings from HITS, PageRank, and SALSA: Existence, uniqueness, and effect of initialization, SIAM J. Sci. Comput., 27, pp. 1181--1201.

[55]

D. Fiala, F. Rousselot, and K. Ježek (2008), PageRank for bibliographic networks, Scientometrics, 76, pp. 135--158.

[56]

M. Fiedler (1973), Algebraic connectivity of graphs, Czechoslovak Math. J., 23, pp. 298--305.

[57]

D. Fogaras (2003), Where to start browsing the web?, in Innovative Internet Community Systems, T. Böhme, G. Heyer, and H. Unger, eds., Lecture Notes in Comput. Sci. 2877, Springer, Berlin, Heidelberg, pp. 65--79.

[58]

K. M. Frahm, A. D. Chepelianskii, and D. L. Shepelyansky (2012), PageRank of integers, J. Phys. A, 45, 405101.

[59]

L. C. Freeman (1977), A set of measures of centrality based on betweenness, Sociometry, 40, pp. 35--41.

[60]

V. Freschi (2007), Protein function prediction from interaction networks using a random walk ranking algorithm, in Proceedings of the 7th IEEE International Conference on Bioinformatics and Bioengineering (BIBE 2007), IEEE, pp. 42--48.

[61]

N. E. Friedkin and E. C. Johnsen (1990), Social influence and opinions, J. Math. Soc., 15, pp. 193--206.

[62]

N. E. Friedkin and E. C. Johnsen (1999), Social influence networks and opinion change, Adv. Group Process., 16, pp. 1--29.

[63]

E. Garfield (1955), Citation indexes for science: A new dimension in documentation through association of ideas, Science, 122, pp. 108--111.

[64]

E. Garfield and I. H. Sher (1963), New factors in the evaluation of scientific literature through citation indexing, Amer. Documentation, 14, pp. 195--201.

[65]

D. F. Gleich, P. G. Constantine, A. Flaxman, and A. Gunawardana (2010a), Tracking the random surfer: Empirically measured teleportation parameters in PageRank, in Proceedings of the 19th International Conference on the World Wide Web, WWW '10, ACM Press, New York, pp. 381--390.

[66]

D. F. Gleich, P. Glynn, G. H. Golub, and C. Greif (2007), Three results on the PageRank vector: Eigenstructure, sensitivity, and the derivative, in Web Information Retrieval and Linear Algebra Algorithms, A. Frommer, M. W. Mahoney, and D. B. Szyld, eds., Dagstuhl Seminar Proceedings 07071, Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany.

[67]

D. F. Gleich, A. P. Gray, C. Greif, and T. Lau (2010b), An inner-outer iteration for PageRank, SIAM J. Sci. Comput., 32, pp. 349--371.

[68]

D. F. Gleich, L.-H. Lim, and Y. Yu (2014), Multilinear PageRank, arXiv preprint, cs.NA, 1409.1465.

[69]

D. F. Gleich and M. M. Mahoney (2014), Anti-differentiating approximation algorithms: A case study with min-cuts, spectral, and flow, in Proceedings of the 31st International Conference on Machine Learning (ICML), pp. 1018--1025.

[70]

D. F. Gleich and M. Polito (2007), Approximating personalized PageRank with minimal use of webgraph data, Internet Math., 3, pp. 257--294.

[71]

D. F. Gleich and R. A. Rossi (2014), A dynamical system for PageRank with time-dependent teleportation, Internet Math., 10, pp. 188--217.

[72]

D. F. Gleich, L. Zhukov, and P. Berkhin (2004), Fast Parallel PageRank: A Linear System Approach, Tech. Report YRL-2004-038, Yahoo! Research Labs, research.yahoo.com/publication/YRL-2004-035.pdf.

[73]

G. Golub and C. Greif (2006), An Arnoldi-type algorithm for computing PageRank, BIT, 46, pp. 759--771.

[74]

M. Gori and A. Pucci (2007), ItemRank: A random-walk based scoring algorithm for recommender engines, in Proceedings of the 20th International Joint Conference on Artifical Intelligence, IJCAI'07, San Francisco, CA, Morgan Kaufmann, pp. 2766--2771.

[75]

A. Y. Govan, C. D. Meyer, and R. Albright (2008), Generalizing Google's PageRank to rank national football league teams, in Proceedings of the SAS Global Forum 2008, SAS paper 151-2008.

[76]

P. Grindrod and D. J. Higham (2014), A dynamical systems view of network centrality, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 470, 2013083.

[77]

Z. Gyöngyi, H. Garcia-Molina, and J. Pedersen (2004), Combating web spam with TrustRank, in Proceedings of the 30th International Very Large Database Conference, Toronto, Canada, pp. 576--587.

[78]

A. Halu, R. J. Mondragón, P. Panzarasa, and G. Bianconi (2013), Multiplex PageRank, PLoS ONE, 8, e78293.

[79]

T. H. Haveliwala (2002), Topic-sensitive PageRank, in Proceedings of the 11th International Conference on the World Wide Web, WWW02, ACM, pp. 517--526.

[80]

D. J. Higham (2005), Google PageRank as mean playing time for pinball on the reverse web, Appl. Math. Lett., 18, pp. 1359--1362.

[81]

R. A. Horn and S. Serra-Capizzano (2007), A general setting for the parametric Google matrix, Internet Math., 3, pp. 385--411.

[82]

A. Hotho, R. Jäschke, C. Schmitz, and G. Stumme (2006), Information retrieval in folksonomies: Search and ranking, in Proceedings of the 3rd European Semantic Web Conference, Y. Sure and J. Domingue, eds., Lecture Notes in Comput. Sci. 4011, Springer, Berlin, Heidelberg, pp. 411--426.

[83]

B. A. Huberman, P. L. T. Pirolli, J. E. Pitkow, and R. M. Lukose (1998), Strong regularities in World Wide Web surfing, Science, 280, pp. 95--97.

[84]

A. Jain and P. Pantel (2010), FactRank: Random walks on a web of facts, in Proceedings of the 23rd International Conference on Computational Linguistics, COLING '10, Association for Computational Linguistics, Stroudsburg, PA, pp. 501--509.

[85]

A. Java (2007), Twitter Social Network Analysis, UMBC ebiquity blog, http://ebiquity.umbc.edu/ blogger/2007/04/19/twitter-social-network-analysis/.

[86]

A. Java, P. Kolari, T. Finin, and T. Oates (2006), Modeling the Spread of Influence on the Blogosphere, Tech. Report UMBC TR-CS-06-03, University of Maryland, Baltimore, MD.

[87]

G. Jeh and J. Widom (2002), SimRank: A measure of structural-context similarity, in Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '02, ACM, New York, pp. 538--543.

[88]

K. Jezek, D. Fiala, and J. Steinberger (2008), Exploration and evaluation of citation networks, in Proceedings of the 12th International Conference on Electronic Publishing, L. Chan and S. Mornatti, eds., pp. 351--362.

[89]

B. Jiang (2009), Ranking spaces for predicting human movement in an urban environment, Int. J. Geogr. Inf. Sci., 23, pp. 823--837.

[90]

B. Jiang, S. Zhao, and J. Yin (2008), Self-organized natural roads for predicting traffic flow: A sensitivity study, J. Statist. Mech., 2008, P07008.

[91]

B.-B. Jiang, J.-G. Wang, J.-F. Xiao, and Y. Wang (2009), Gene prioritization for type 2 diabetes in tissue-specific protein interaction networks, in Proceedings of the Third International Symposium on Optimization and Systems Biology, World Publishing Corporation, pp. 319--328.

[92]

Y. Jing and S. Baluja (2008), VisualRank: Applying PageRank to large-scale image search, IEEE Trans. Pattern Anal. Mach. Intell., 30, pp. 1877--1890.

[93]

M. Jockers (2012), Computing and visualizing the 19th-century literary genome, in Digital Humanities Conference 2012, pp. 242--244.

[94]

S. Kamvar (2010), Numerical Algorithms for Personalized Search in Self-Organizing Information Networks, Princeton University Press, Princeton, NJ.

[95]

S. Kamvar, T. Haveliwala, C. Manning, and G. Golub (2003a), Exploiting the Block Structure of the Web for Computing PageRank, Technical Report 2003-17, Stanford InfoLab, Stanford, CA.

[96]

S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and G. H. Golub (2003b), Extrapolation methods for accelerating PageRank computations, in Proceedings of the 12th International Conference on the World Wide Web, ACM, New York, pp. 261--270.

[97]

L. Katz (1953), A new status index derived from sociometric analysis, Psychometrika, 18, pp. 39--43.

[98]

J. P. Keener (1993), The Perron--Frobenius theorem and the ranking of football teams, SIAM Rev., 35, pp. 80--93.

[99]

D. Kempe, J. Kleinberg, and E. Tardos (2003), Maximizing the spread of influence through a social network, in Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '03, ACM, New York, pp. 137--146.

[100]

D. Kempe, J. Kleinberg, and E. Tardos (2005), Influential nodes in a diffusion model for social networks, in Proceedings of the 32nd International Conference on Automata, Languages and Programming, ICALP'05, Springer-Verlag, Berlin, Heidelberg, pp. 1127--1138.

[101]

J. Kepner and J. Gilbert, eds. (2011), Graph Algorithms in the Language of Linear Algebra, SIAM, Philadelphia.

[102]

M. Kim, R. Sumbaly, and S. Shah (2013), Root cause detection in a service-oriented architecture, in Proceedings of the ACM SIGMETRICS/International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS '13, ACM, New York, pp. 93--104.

[103]

J. M. Kleinberg (1999), Authoritative sources in a hyperlinked environment, J. ACM, 46, pp. 604--632.

[104]

T. G. Kolda and M. J. Procopio (2009), Generalized BadRank with Graduated Trust, Tech. Report SAND2009-6670, Sandia National Laboratories, Albuquerque, NM.

[105]

G. Kollias, E. Gallopoulos, and A. Grama (2013), Surfing the network for ranking by multidamping, IEEE Trans. Knowledge Data Engrg., 26, pp. 2323--2336.

[106]

G. Kollias, S. Mohammadi, and A. Grama (2012), Network similarity decomposition (NSD): A fast and scalable approach to network alignment, IEEE Trans. Knowledge Data Engrg., 24, pp. 2232--2243.

[107]

R. I. Kondor and J. D. Lafferty (2002), Diffusion kernels on graphs and other discrete input spaces, in Proceedings of the Nineteenth International Conference on Machine Learning, ICML '02, Morgan Kaufmann, San Francisco, CA, pp. 315--322.

[108]

E.-M. Kontopoulou, M. Predari, T. Kostakis, and E. Gallopoulos (2012), Graph and matrix metrics to analyze ergodic literature for children, in Proceedings of the 23rd ACM Conference on Hypertext and Social Media, HT '12, ACM, New York, pp. 133--142.

[109]

D. Koschützki, K. A. Lehmann, L. Peeters, S. Richter, D. Tenfelde-Podehl, and O. Zlotowski (2005), Centrality indices, in Network Analysis: Methodological Foundations, U. Brandes and T. Erlebach, eds., Lecture Notes in Comput. Sci. 3418, Springer, New York, pp. 16--61.

[110]

J. Kunegis and A. Lommatzsch (2009), Learning spectral graph transformations for link prediction, in Proceedings of the 26th Annual International Conference on Machine Learning, ICML '09, ACM, New York, pp. 561--568.

[111]

H. Kwak, C. Lee, H. Park, and S. Moon (2010), What is Twitter, a social network or a news media?, in Proceedings of the 19th International Conference on the World Wide Web, WWW '10, ACM, New York, pp. 591--600.

[112]

A. N. Langville and C. D. Meyer (2004), Deeper inside PageRank, Internet Math., 1, pp. 335--380.

[113]

A. N. Langville and C. D. Meyer (2006), Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, Princeton, NJ.

[114]

A. N. Langville and C. D. Meyer (2012), Who's \#1? The Science of Rating and Ranking, Princeton University Press, Princeton, NJ.

[115]

C. P. Lee, G. H. Golub, and S. A. Zenios (2007), A two-stage algorithm for computing PageRank and multistage generalizations, Internet Math., 4, pp. 299--327.

[116]

S. Levy (2010), How Google's algorithm rules the web, Wired Magazine, 17, www.wired.com. Retrieved on 2015-01-27.

[117]

D. Liben-Nowell and J. Kleinberg (2006), The link-prediction problem for social networks, J. Amer. Soc. Inform. Sci. Tech., 58, pp. 1019--1031.

[118]

X. Liu, J. Bollen, M. L. Nelson, and H. Van de Sompel (2005), Co-authorship networks in the digital library research community, Inform. Process. Management, 41, pp. 1462--1480.

[119]

Y. Liu, B. Gao, T.-Y. Liu, Y. Zhang, Z. Ma, S. He, and H. Li (2008), BrowseRank: Letting web users vote for page importance, in Proceedings of the 31st Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR '08, ACM, New York, pp. 451--458.

[120]

L. Lü, Y.-C. Zhang, C. H. Yeung, and T. Zhou (2011), Leaders in social networks: The Delicious case, PLoS ONE, 6, e21202.

[121]

N. Ma, J. Guan, and Y. Zhao (2008), Bringing PageRank to the citation analysis, Inform. Process. Management, 44, pp. 800--810.

[122]

M. W. Mahoney, L. Orecchia, and N. K. Vishnoi (2012), A local spectral method for graphs: With applications to improving graph partitions and exploring data graphs locally, J. Mach. Learn. Res., 13, pp. 2339--2365.

[123]

X. Meng (2009), Computing BookRank via Social Cataloging, http://cads.stanford.edu/projects/presentations/2009visit/bookrank.pdf.

[124]

C. D. Meyer (2000), Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia.

[125]

J. C. Miller, G. Rae, F. Schaefer, L. A. Ward, T. LoFaro, and A. Farahat (2001), Modifications of Kleinberg's HITS algorithm using matrix exponentiation and web log records, in Proceedings of the 24th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR '01, ACM, New York, pp. 444--445.

[126]

B. L. Mooney, L. R. Corrales, and A. E. Clark (2012), MoleculaRnetworks: An integrated graph theoretic and data mining tool to explore solvent organization in molecular simulation, J. Comput. Chem., 33, pp. 853--860.

[127]

J. L. Morrison, R. Breitling, D. J. Higham, and D. R. Gilbert (2005), GeneRank: Using search engine technology for the analysis of microarray experiments, BMC Bioinformatics, 6, p. 233.

[128]

M. A. Najork, H. Zaragoza, and M. J. Taylor (2007), HITS on the web: How does it compare?, in Proceedings of the 30th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR2007, ACM, New York, pp. 471--478.

[129]

Z. Nie, Y. Zhang, J.-R. Wen, and W.-Y. Ma (2005), Object-level ranking: Bringing order to web objects, in Proceedings of the 14th International Conference on World Wide Web, WWW '05, ACM, New York, pp. 567--574.

[130]

L. Orecchia and M. W. Mahoney (2011), Implementing regularization implicitly via approximate eigenvector computation, in Proceedings of the 28th International Conference on Machine Learning, ICML-11, L. Getoor and T. Scheffer, eds., ACM, New York, pp. 121--128.

[131]

G. Osipenko (2007), Dynamical Systems, Graphs, and Algorithms, Springer, New York.

[132]

L. Page, S. Brin, R. Motwani, and T. Winograd (1999), The PageRank Citation Ranking: Bringing Order to the Web, Tech. Report 1999-66, Stanford University, Stanford, CA.

[133]

J.-Y. Pan, H.-J. Yang, C. Faloutsos, and P. Duygulu (2004), Automatic multimedia cross-modal correlation discovery, in Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '04, ACM, New York, pp. 653--658.

[134]

G. Pinski and F. Narin (1976), Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics, Inform. Process. Management, 12, pp. 297--312.

[135]

A. Pothen, H. D. Simon, and K.-P. Liou (1990), Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Appl., 11, pp. 430--452.

[136]

L. Pretto (2002), A theoretical analysis of Google's PageRank, in Proceedings of the 9th International Symposium on String Processing and Information Retrieval, SPIRE 2002, Springer-Verlag, London, pp. 131--144.

[137]

F. Radicchi (2011), Who is the best player ever? A complex network analysis of the history of professional tennis, PLoS ONE, 6, e17249.

[138]

G. Sabidussi (1966), The centrality index of a graph, Psychometrika, 31, pp. 581--603.

[139]

S. E. Schaeffer (2007), Graph clustering, Comput. Sci. Rev., 1, pp. 27--64.

[140]

A. Schlote, E. Crisostomi, S. Kirkland, and R. Shorten (2012), Traffic modelling framework for electric vehicles, Internat. J. Control, 85, pp. 880--897.

[141]

S. Serra-Capizzano (2005), Jordan canonical form of the Google matrix: A potential contribution to the PageRank computation, SIAM J. Matrix Anal. Appl., 27, pp. 305--312.

[142]

D. L. Shepelyansky and O. V. Zhirov (2010), Google matrix, dynamical attractors, and Ulam networks, Phys. Rev. E, 81, 036213.

[143]

R. Singh, J. Xu, and B. Berger (2007), Pairwise global alignment of protein interaction networks by matching neighborhood topology, in Proceedings of the 11th Annual International Conference on Research in Computational Molecular Biology (RECOMB), Oakland, CA, Lecture Notes in Comput. Sci. 4453, Springer, Berlin, Heidelberg, pp. 16--31.

[144]

M. Sobek (2003), PR0 - Google's PageRank $0$ Penalty, http://pr.efactory.de/e-pr0.shtml. Accessed 2013-09-19.

[145]

Y. Song, D. Zhou, and L.-w. He (2012), Query suggestion by constructing term-transition graphs, in Proceedings of the Fifth ACM International Conference on Web Search and Data Mining, WSDM '12, ACM, New York, pp. 353--362.

[146]

F. Spezzano, V. S. Subrahmanian, and A. Mannes (2014), Reshaping terrorist networks, Commun. ACM, 57, pp. 60--69.

[147]

O. Sporns (2002), Networks analysis, complexity, and brain function, Complex., 8, pp. 56--60.

[148]

O. Sporns (2011), Networks of the Brain, The MIT Press, Cambridge, MA.

[149]

W. J. Stewart (1994), Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Princeton, NJ.

[150]

J. J. Sylvester (1878), Chemistry and algebra, Nature, 17, p. 284.

[151]

J. A. Tomlin (2003), A new paradigm for ranking pages on the world wide web, in Proceedings of the 12th International Conference on the World Wide Web, WWW '03, ACM, New York, pp. 350--355.

[152]

H. Tong, C. Faloutsos, and J.-Y. Pan (2006), Fast random walk with restart and its applications, in Proceedings of the Sixth International Conference on Data Mining, ICDM '06, IEEE Computer Society, Washington, DC, pp. 613--622.

[153]

S. Vigna (2005), TruRank: Taking PageRank to the limit, in Special Interest Tracks and Posters of the 14th International Conference on the World Wide Web, WWW '05, ACM, New York, pp. 976--977.

[154]

S. Vigna (2009), Spectral Ranking, arXiv preprint, cs.IR, 0912.0238.

[155]

K. Voevodski, S.-H. Teng, and Y. Xia (2009), Spectral affinity in protein networks, BMC Syst. Biol., 3, p. 112.

[156]

D. Walker, H. Xie, K.-K. Yan, and S. Maslov (2007), Ranking scientific publications using a model of network traffic, J. Statist. Mech., 6, P06010.

[157]

W. Y. Wang, K. Mazaitis, and W. W. Cohen (2013), Programming with personalized PageRank: A locally groundable first-order probabilistic logic, in Proceedings of the 22nd ACM International Conference on Conference on Information and Knowledge Management, CIKM '13, ACM, New York, pp. 2129--2138.

[158]

J. Weng, E.-P. Lim, J. Jiang, and Q. He (2010), TwitterRank: Finding topic-sensitive influential twitterers, in Proceedings of the Third ACM International Conference on Web Search and Data Mining, WSDM '10, ACM, New York, pp. 261--270.

[159]

J. D. West, T. C. Bergstrom, and C. T. Bergstrom (2010), The Eigenfactor metrics: A network approach to assessing scholarly journals, College & Res. Libraries, 71, pp. 236--244.

[160]

R. S. Wills and I. C. F. Ipsen (2009), Ordinal ranking for Google's PageRank, SIAM J. Matrix Anal. Appl., 30, pp. 1677--1696.

[161]

C. Winter, G. Kristiansen, S. Kersting, J. Roy, D. Aust, T. Knösel, P. Rümmele, B. Jahnke, V. Hentrich, F. Rückert, M. Niedergethmann, W. Weichert, M. Bahra, H. J. Schlitt, U. Settmacher, H. Friess, M. Büchler, H.-D. Saeger, M. Schroeder, C. Pilarsky, and R. Grützmann (2012), Google goes cancer: Improving outcome prediction for cancer patients by network-based ranking of marker genes, PLoS Comput. Biol., 8, e1002511.

[162]

A. D. Wissner-Gross (2006), Preparation of topical reading lists from the link structure of Wikipedia, in ICALT '06: Proceedings of the Sixth IEEE International Conference on Advanced Learning Technologies, IEEE Computer Society, Washington, DC, pp. 825--829.

[163]

W. Xing and A. Ghorbani (2004), Weighted PageRank algorithm, in Proceedings of the Second Annual Conference on Communication Networks and Services Research, IEEE, pp. 305--314.

[164]

H. Yang, I. King, and M. R. Lyu (2007), DiffusionRank: A possible penicillin for web spamming, in Proceedings of the 30th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR '07, ACM, New York, pp. 431--438.

[165]

A. O. Zhirov, O. V. Zhirov, and D. L. Shepelyansky (2010), Two-dimensional ranking of Wikipedia articles, Eur. Phys. J. B, 77, pp. 523--531.

[166]

D. Zhou, O. Bousquet, T. N. Lal, J. Weston, and B. Schölkopf (2003), Learning with local and global consistency, in Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, and B. Schölkopf, eds., MIT Press, Cambridge, MA, pp. 169--176

[167]

D. Zhou, J. Huang, and B. Schölkopf (2005), Learning from labeled and unlabeled data on a directed graph, in Proceedings of the 22nd International Conference on Machine Learning, ICML '05, ACM, New York, pp. 1036--1043.

[168]

X.-N. Zuo, R. Ehmke, M. Mennes, D. Imperati, F. X. Castellanos, O. Sporns, and M. P. Milham (2012), Network centrality in the human functional connectome, Cerebral Cortex, 22, pp. 1862--1875.

Cited By

Liao MLi CLi RWang G(2025)Efficient Index Maintenance for Effective Resistance Computation on Evolving GraphsProceedings of the ACM on Management of Data10.1145/37096863:1(1-27)Online publication date: 11-Feb-2025
https://dl.acm.org/doi/10.1145/3709686
Wang JLi PLiu YXiong XZhang YLv Z(2025)Risk identification of listed companies violation by integrating knowledge graph and multi-source risk factorsEngineering Applications of Artificial Intelligence10.1016/j.engappai.2024.109774141:COnline publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1016/j.engappai.2024.109774
Bentbib ABoubekraoui MJbilou K(2025)Extrapolation methods for multilinear PageRankNumerical Algorithms10.1007/s11075-024-01823-x98:2(1013-1043)Online publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1007/s11075-024-01823-x
Show More Cited By

Index Terms

PageRank Beyond the Web

Index terms have been assigned to the content through auto-classification.

Recommendations

Beyond PageRank: machine learning for static ranking
WWW '06: Proceedings of the 15th international conference on World Wide Web

Since the publication of Brin and Page's paper on PageRank, many in the Web community have depended on PageRank for the static (query-independent) ordering of Web pages. We show that we can significantly outperform PageRank using features that are ...
PageRank revisited

PageRank, one part of the search engine Google, is one of the most prominent link-based rankings of documents in the World Wide Web. Usually it is described as a Markov chain modeling a specific random surfer. In this article, an alternative ...
Multilinear PageRank

In this paper, we first extend the celebrated PageRank modification to a higher-order Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a ...

Comments

Information & Contributors

Information

Published In

cover image SIAM Review

SIAM Review Volume 57, Issue 3

DOI:10.1137/siread.57.3

Issue’s Table of Contents

© 2015, Society for Industrial and Applied Mathematics.

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2015

Author Tags

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

85
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 20 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Liao MLi CLi RWang G(2025)Efficient Index Maintenance for Effective Resistance Computation on Evolving GraphsProceedings of the ACM on Management of Data10.1145/37096863:1(1-27)Online publication date: 11-Feb-2025
https://dl.acm.org/doi/10.1145/3709686
Wang JLi PLiu YXiong XZhang YLv Z(2025)Risk identification of listed companies violation by integrating knowledge graph and multi-source risk factorsEngineering Applications of Artificial Intelligence10.1016/j.engappai.2024.109774141:COnline publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1016/j.engappai.2024.109774
Bentbib ABoubekraoui MJbilou K(2025)Extrapolation methods for multilinear PageRankNumerical Algorithms10.1007/s11075-024-01823-x98:2(1013-1043)Online publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1007/s11075-024-01823-x
Li YLu TLi WZhang P(2024)HCCKshellInformation Processing and Management: an International Journal10.1016/j.ipm.2024.10368161:3Online publication date: 2-Jul-2024
https://dl.acm.org/doi/10.1016/j.ipm.2024.103681
Sun WXu JZhang WLi XZeng YZhang P(2024)Funnel graph neural networks with multi-granularity cascaded fusing for protein–protein interaction predictionExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.125030257:COnline publication date: 10-Dec-2024
https://dl.acm.org/doi/10.1016/j.eswa.2024.125030
Han DKim DHan KYi M(2024)Keyword-enhanced recommender system based on inductive graph matrix completionEngineering Applications of Artificial Intelligence10.1016/j.engappai.2023.107499128:COnline publication date: 14-Mar-2024
https://dl.acm.org/doi/10.1016/j.engappai.2023.107499
Zhang YWu G(2024)Two Accelerated Non-backtracking PageRank Algorithms for Large-scale NetworksJournal of Scientific Computing10.1007/s10915-024-02735-7102:1Online publication date: 16-Nov-2024
https://dl.acm.org/doi/10.1007/s10915-024-02735-7
Chen YLi WChang J(2024)Multi-Linear Pseudo-PageRank for Hypergraph PartitioningJournal of Scientific Computing10.1007/s10915-024-02460-199:1Online publication date: 26-Feb-2024
https://dl.acm.org/doi/10.1007/s10915-024-02460-1
Yang SFountoulakis KKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Weighted flow diffusion for local graph clustering with node attributesProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3620045(39252-39276)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3620045
Hu RDu YHu JLi H(2023)Cross-community shortcut detection based on network representation learning and structural featuresIntelligent Data Analysis10.3233/IDA-21651327:3(709-732)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.3233/IDA-216513
Show More Cited By

View Options

View options

Figures

Tables

Media

View Issue’s Table of Contents