Estimating and sampling graphs with multidimensional random walks

Proceedings of the ACM SIGCOMM Internet Measurement Conference, IMC

Volumn , Issue , 2010, Pages 390-403

  Ribeiro, Bruno ^a   Towsley, Don ^a  

^a University of Massachusetts Amherst   (United States)

Author keywords

Assortativity; Estimates; Frontier sampling; Global clustering coefficient; MCMC; Power laws; Random walks

Indexed keywords

COMPLEX NETWORKS; DATA MINING; ESTIMATION; GRAPH THEORY; RANDOM ERRORS; RANDOM PROCESSES; SAMPLING;

ASSORTATIVITY; CLUSTERING COEFFICIENT; ESTIMATE; FRONTIER SAMPLING; GLOBAL CLUSTERING; GLOBAL CLUSTERING COEFFICIENT; MCMC; POWER-LAW; RANDOM VERTEX; RANDOM WALK;

GRAPHIC METHODS;

EID: 78650856898     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1879141.1879192     Document Type: Conference Paper

References (38)

1. Dimitris Achlioptas, Aaron Clauset, David Kempe, and Cristopher Moore. On the bias of traceroute sampling: Or, power-law degree distributions in regular graphs. J. ACM, 56(4):1-28, 2009.
2. Chen Avin and Bhaskar Krishnamachari. The power of choice in random walks: An empirical study. Comput. Netw., 52(1):44-60, 2008.
3. P. Balister, B. Bollobás, and A. Stacey. Dependent percolation in two dimensions. Prob. Theory and Related Fields, 117(4):495-513, 2000.
4. Ziv Bar-Yossef and Maxim Gurevich. Random sampling from a search engine's index. J. ACM, 55(5):1-74, 2008.
5. A.-L. Barabási and R. Albert. Emergence of scaling in random networks. Science, 286:509-512, 1999.
6. Nabhendra Bisnik and Alhussein A. Abouzeid. Optimizing random walk search algorithms in p2p networks. Computer Networks, 51(6):1499-1514, 2007.
7. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang. Complex networks: Structure and dynamics. Physics Reports, 424(4-5):175-308, 2006.
8. Christos G. Cassandras and Stephane Lafortune. Introduction to Discrete Event Systems. Springer-Verlag, Inc., 2006.
9. Fang Chen, László Lovász, and Igor Pak. Lifting Markov chains to speed up mixing. In Proc. of STOC, pages 275-281, 1999.
10. Junghoo Cho and Hector Garcia-Molina. Parallel crawlers. In Proc. of the WWW, pages 124-135, 2002.
11. Nathan Eagle, Alex S. Pentland, and David Lazer. Inferring friendship network structure by using mobile phone data. PNAS, 106(36):15274-15278, August 2009.
12. W. Feller. An Introduction to Probability Theory and its Applications, volume 1. John Wiley & Sons, New York, 3rd edition, 1968.
13. Coperative Association for Internet Data Analysis. CAIDA's Internet topology data kit #0304, 2003.
14. Charles J. Geyer. Practical Markov Chain Monte Carlo. Statistical Science, 7(4):473-483, 1992.
15. Minas Gjoka, Maciej Kurant, Carter T. Butts, and Athina Markopoulou. A walk in Facebook: Uniform sampling of users in online social networks. In Proc. of the IEEE Infocom, March 2010.
16. Christos Gkantsidis, Milena Mihail, and Amin Saberi. Random walks in peer-to-peer networks: algorithms and evaluation. Perform. Eval., 63(3):241-263, March 2006.
17. Monika R. Henzinger, Allan Heydon, Michael Mitzenmacher, and Marc Najork. On near-uniform url sampling. In Proceedings of the WWW, pages 295-308, 2000.
18. Marlom A. Konrath, Marinho P. Barcellos, and Rodrigo B. Mansilha. Attacking a swarm with a band of liars: evaluating the impact of attacks on bittorrent. In P2P '07: Proceedings of the Seventh IEEE International Conference on Peer-to-Peer Computing, pages 37-44, Washington, DC, USA, 2007. IEEE Computer Society.
19. Jure Leskovec and Christos Faloutsos. Sampling from large graphs. In Proc. of the KDD, pages 631-636, 2006.
20. Jure Leskovec, Kevin J. Lang, Anirban Dasgupta, and Michael W. Mahoney. Statistical properties of community structure in large social and information networks. In Proc. of the WWW, pages 695-704, 2008.
21. David A. Levin, Yuval Peres, and Elizabeth L. Wilmer. Markov Chains and Mixing Times. AMS, 2009.
22. L. Lovász. Random walks on graphs: a survey. Combinatorics, 2:1-46, 1993.
23. Laurent Massoulié, Erwan Le Merrer, Anne-Marie Kermarrec, and Ayalvadi Ganesh. Peer counting and sampling in overlay networks: random walk methods. In Proc. of the PODC, pages 123-132, 2006.
24. Courtney McKnight, Don Des Jarlais, Heidi Bramson, Lisa Tower, Abu S. Abdul-Quader, Chris Nemeth, and Douglas Heckathorn. Respondent-driven sampling in a study of drug users in New York City: Notes from the field. Journal of Urban Health, 83(6):154-159, 2006.
25. Sean Meyn and Richard L. Tweedie. Markov Chains and Stochastic Stability. Cambridge University Press, 2009.
26. Alan Mislove, Massimiliano Marcon, Krishna P. Gummadi, Peter Druschel, and Bobby Bhattacharjee. Measurement and Analysis of Online Social Networks. In Proc. of the IMC, October 2007.
27. M. E. J. Newman. Assortative mixing in networks. Phys. Rev. Lett., 89(20):208701, Oct 2002.
28. M. E. J. Newman. The structure and function of complex networks. SIAM Review, 45(2):167-256, 2003.
29. Amir H. Rasti, Mojtaba Torkjazi, Reza Rejaie, Nick Duffield, Walter Willinger, and Daniel Stutzbach. Respondent-driven sampling for characterizing unstructured overlays. In Proc. of the IEEE Infocom, pages 2701-2705, April 2009.
30. Bruno Ribeiro, William Gauvin, Benyuan Liu, and Don Towsley. On MySpace account spans and double Pareto-like distribution of friends. In IEEE Infocom 2010 Network Science Workshop, Mar 2010.
31. Bruno Ribeiro and Donald Towsley. Estimating and sampling graphs with multidimensional random walks. arXiv:1002.1751v2, 2010.
32. Christian P. Robert and George Casella. Monte Carlo Statistical Methods. Springer-Verlag, 2nd edition, 2005.
33. Paat Rusmevichientong, David M. Pennock, Steve Lawrence, and Lee C. Giles. Methods for sampling pages uniformly from the world wide web. In AAAI Fal l Symposium on Using Uncertainty Within Computation, pages 121-128, 2001.
34. Thomas Schank and Dorothea Wagner. Approximating clustering-coefficient and transitivity. Journal of Graph Algorithms and Applications, 9(2):265-275, 2004.
35. Daniel Stutzbach, Reza Rejaie, Nick Duffield, Subhabrata Sen, and Walter Willinger. On unbiased sampling for unstructured peer-to-peer networks. IEEE/ACM Trans. Netw., 17(2):377-390, 2009.
36. Erik Volz and Douglas D. Heckathorn. Probability based estimation theory for Respondent-Driven Sampling. Journal of Official Statistics, 2008.
37. D.J. Watts and S.H. Strogatz. Collective dynamics of "small world" networks. Nature, 393:440-442, June 1998.
38. Ming Zhong and Kai Shen. Random walk based node sampling in self-organizing networks. SIGOPS Oper. Syst. Rev., 40(3):49-55, 2006.