A fast algorithm to find all high degree vertices in power law graphs

WWW'12 - Proceedings of the 21st Annual Conference on World Wide Web Companion

Volumn , Issue , 2012, Pages 1007-1016

  Cooper, Colin ^a   Radzik, Tomasz ^a   Siantos, Yiannis ^a  

^a KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Graph sampling; Random walks; Weighted random walks

Indexed keywords

ARBITRARY VERTICES; CONSTANT PARAMETERS; COVER TIME; DEGREE SEQUENCE; EXHAUSTIVE SEARCH; EXPERIMENTAL TEST; FAST ALGORITHMS; HIGH PROBABILITY; LARGE GRAPHS; LARGE SIZES; ONLINE SOCIAL NETWORKS; POSITIVE CONSTANT; POWER LAW GRAPHS; PREFERENTIAL ATTACHMENT MODEL; PREFERENTIAL ATTACHMENTS; RANDOM WALK; REAL-WORLD NETWORKS; REPRESENTATIVE SAMPLE; SAMPLING METHOD; SIMPLE RANDOM WALK; SOCIAL NETWORKS; UNDERLYING GRAPHS;

GRAPHIC METHODS; RANDOM PROCESSES; WORLD WIDE WEB;

GRAPH THEORY;

EID: 84861038937     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2187980.2188235     Document Type: Conference Paper

References (26)

1. D. Achlioptas, A. Clauset, D. Kempe, and C. Moore. On the bias of traceroute sampling: or, power-law degree distributions in regular graphs. J. ACM, 56(4), 2009.
2. D. Aldous and J. A. Fill. Reversible Markov chains and random walks on graphs. http://stat-www.berkeley.edu/pub/users/aldous/RWG/book.html, 1995.
3. R. Baeza-Yates, C. Castillo, M. Marin, and A. Rodriguez. Crawling a country: Better strategies than breadth-first for web page ordering. In Proceedings of the 14th international conference on World Wide Web / Industrial and Practical Experience Track, pages 864-872. ACM Press, 2005.
4. A. Barabási and R. Albert. Emergence of scaling in random networks. Science, number 5439 in Volume 286, pages 509-512, 1999.
5. B. Bollobás and O. Riordan. Handbook of Graphs and Networks: Mathematical results on scale-free graphs, pages 1-32. S. Bornholdt, H. Schuster (eds), Wiley-VCH, 2002.
6. B. Bollobás and O. Riordan. The diameter of a scale-free random graph. Combinatorica, 24:5-34, 2004.
7. B. Bollobás, O. Riordan, J. Spencer, and G. Tusnády. The degree sequence of a scale-free random graph process. Random Structures and Algorithms, 18:279-290, 2001.
8. M. Brautbar and M. Kearns. Local algorithms for finding interesting individuals in large networks. In Proceedings of ICS 2010, pages 188-199, 2010.
9. A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tomkins, and J. Wiener. Graph structure in the web: experiments and models. In Proceedings of the Ninth International World-Wide Web Conference WWW9, Amsterdam 2000. http://www.www9.org/w9cdrom/160/160.html.
10. C. Cooper. Classifying special interest groups in web graphs. In Proc. RANDOM 2002: Randomization and Approximation Techniques in Computer Science, pages 263-275, 2002.
11. C. Cooper. The age specific degree distribution of web-graphs. Combinatorics Probability and Computing, 15:637-661, 2006.
12. C. Cooper and A. Frieze. A general model web graphs. In Random Structures and Algorithms, vol. 22(3), pages 311-335, 2003.
13. C. Cooper and A. Frieze. The cover time of the preferential attachment graphs. Journal of Combinatorial Theory, B(97):269-290, 2007.
14. S. Dill, R. Kumar, K. S. Mccurley, S. Rajagopalan, D. Sivakumar, and A. Tomkins. Self-similarity in the web. ACM Trans. Internet Technol., 2:205-223, August 2002.
15. M. E. E. Drinea and M. Mitzenmacher. Variations on random graph models for the web. Tech. report, Harvard University, Dept. of Computer Science, 2001.
16. M. Faloutsos, P. Faloutsos, and C. Faloutsos. On power-law relationships of the Internet topology. In Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication, SIGCOMM '99, pages 251-262, New York, NY, USA, 1999. ACM.
17. A. D. Flaxman and J. Vera. Bias reduction in traceroute sampling - towards a more accurate map of the Internet. In Proceedings of WAW 2007, pages 1-15, 2007.
18. M. Gjoka, M. Kurant, C. T. Butts, and A. Markopoulou. A walk in Facebook: Uniform sampling of users in online social networks. CoRR, abs/0906.0060, 2009.
19. S. Ikeda, I. Kubo, N. Okumoto, and M. Yamashita. Impact of Local Topological Information on Random Walks on Finite Graphs. In Proceedings of ICALP 2003, pages 1054-1067.
20. J. M. Kleinberg, R. Kumar, P. Raghavan, S. Rajagopalan, and A. S. Tomkins. The Web as a graph: measurements, models, and methods. In Proceedings of the 5th Annual International Conference on Computing and Combinatorics, COCOON'99, pages 1-17, 1999.
21. J. Leskovec and C. Faloutsos. Sampling from large graphs. In Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 631-636, 2006.
22. L. Lovász. Random walks on graphs: A survey. Bolyai Society Mathematical Studies, 2:353-397, 1996.
23. R. Albert and A.-L. Barabási. Statistical mechanics of complex networks. In Reviews Of Modern Physics, vol. 74, pages 47-97, 2002.
24. A. H. Rasti, M. Torkjazi, R. Rejaie, N. Duffield, W. Willinger, and D. Stutzbach. Evaluating sampling techniques for large dynamic graphs. Technical Report CIS-TR-08-01, Department of Computer and Information Science, University of Oregon, September 2008.
25. S. Redner. How popular is your paper? An empirical study of the citation distribution. In European Physical Journal B vol. 4(2), pages 131-134, 1998.
26. D. Stutzbach, R. Rejaie, N.G. Duffield, S. Sen and W. Willinger. On unbiased sampling for unstructured peer-to-peer networks. In Proceedings of the 6th ACM SIGCOMM Conference on Internet Measurement -IMC 2006, pages 27-40, 2006.