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Data Mining and Knowledge Discovery

, Volume 19, Issue 2, pp 194–209 | Cite as

RTG: a recursive realistic graph generator using random typing

  • Leman Akoglu
  • Christos Faloutsos
Article

Abstract

We propose a new, recursive model to generate realistic graphs, evolving over time. Our model has the following properties: it is (a) flexible, capable of generating the cross product of weighted/unweighted, directed/undirected, uni/bipartite graphs; (b) realistic, giving graphs that obey eleven static and dynamic laws that real graphs follow (we formally prove that for several of the (power) laws and we estimate their exponents as a function of the model parameters); (c) parsimonious, requiring only four parameters. (d) fast, being linear on the number of edges; (e) simple, intuitively leading to the generation of macroscopic patterns. We empirically show that our model mimics two real-world graphs very well: Blognet (unipartite, undirected, unweighted) with 27 K nodes and 125 K edges; and Committee-to-Candidate campaign donations (bipartite, directed, weighted) with 23 K nodes and 880 K edges. We also show how to handle time so that edge/weight additions are bursty and self-similar.

Keywords

Simulation and modeling Model validation and analysis Graph generators 

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References

  1. Akoglu L, McGlohon M, Faloutsos C (2008) Rtm: laws and a recursive generator for weighted time-evolving graphs. In: ICDMGoogle Scholar
  2. Albert R, Jeong H, Barabasi A-L (1999) Diameter of the world wide web. Nature 401: 130–131CrossRefGoogle Scholar
  3. Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439): 509–512CrossRefMathSciNetGoogle Scholar
  4. Chakrabarti D, Faloutsos C (2006) Graph mining: laws, generators, and algorithms. ACM Comput Surv 38: 1–69CrossRefGoogle Scholar
  5. Chakrabarti D, Zhan Y, Faloutsos C (2004) R-MAT: a recursive model for graph mining. In: Fourth SIAM international conference on data mining, April 2004, Orlando, Florida, USAGoogle Scholar
  6. Conrad B, Mitzenmacher M (2004) Power laws for monkeys typing randomly: the case of unequal probabilities. IEEE Trans Inf Theory 50(7): 1403–1414CrossRefMathSciNetGoogle Scholar
  7. Crovella M, Bestavros A (1996) Self-similarity in world wide web traffic, evidence and possible causes. In: Sigmetrics, pp 160–169Google Scholar
  8. Erdos P, Renyi A (1960) On the evolution of random graphs. Publ Math Inst Hungary Acad Sci 5: 17–61MathSciNetGoogle Scholar
  9. Even-Bar E, Kearns M, Suri S (2007) A network formation game for bipartite exchange economies. In: SODAGoogle Scholar
  10. Fabrikant A, Luthra A, Maneva EN, Papadimitriou CH, Shenker S (2003) On a network creation game. In: PODCGoogle Scholar
  11. Faloutsos M, Faloutsos P, Faloutsos C (1999) On power-law relationships of the internet topology. In: SIGCOMM, pp 251–262Google Scholar
  12. Flake GW, Lawrence S, Giles CL, Coetzee FM (2002) Self-organization and identification of web communities. IEEE Comput 35: 66–71Google Scholar
  13. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. PNAS 99: 7821MATHCrossRefMathSciNetGoogle Scholar
  14. Gomez ME, Santonja V (1998) Self-similarity in i/o workload: analysis and modeling. In: WWCGoogle Scholar
  15. Gribble SD, Manku GS, Roselli D, Brewer EA, Gibson TJ, Miller EL (1998) Self-similarity in file systems. In: SIGMETRICS ’98Google Scholar
  16. Kleinberg JM, Kumar R, Raghavan P, Rajagopalan S, Tomkins AS (1999) AS The Web as a graph: measurements, models and methods. In: Lecture Notes in Computer Science, vol 1627, pp 1–7Google Scholar
  17. Kraetzl MSE, Nickel C (2005) Random dot product graphs: a model for social networks. In: Preliminary manuscriptGoogle Scholar
  18. Laoutaris N, Poplawski LJ, Rajaraman R, Sundaram R, Teng S-H (2008) Bounded budget connection (bbc) games or how to make friends and influence people, on a budget. In: PODCGoogle Scholar
  19. Leskovec J, Chakrabarti D, Kleinberg JM, Faloutsos C (2005) Realistic, mathematically tractable graph generation and evolution, using Kronecker multiplication. In: PKDD, Porto, PortugalGoogle Scholar
  20. Leskovec J, Kleinberg J, Faloutsos C (2005) Graphs over time: densification laws, shrinking diameters and possible explanations. In: ACM SIGKDDGoogle Scholar
  21. Mandelbrot B (1953) An informational theory of the statistical structure of language. Commun TheoryGoogle Scholar
  22. McGlohon M, Akoglu L, Faloutsos C (2008) Weighted graphs and disconnected components: patterns and a generator. In: ACM SIGKDD, Las Vegas, AugGoogle Scholar
  23. Miller GA (1957) Some effects of intermittent silence. Am J Psychol 70: 311–314CrossRefGoogle Scholar
  24. Newman MEJ (2004) Power laws, Pareto distributions and Zipf’s law, DecemberGoogle Scholar
  25. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69: 026113CrossRefGoogle Scholar
  26. Pennock DM, Flake GW, Lawrence S, Glover EJ, Giles CL (2002) Winners donć6t take all: characterizing the competition for links on the web. In: Proceedings of the national academy of sciences, pp 5207–5211Google Scholar
  27. Schwartz MF, Wood DCM (1992) Discovering shared interests among people using graph analysis of global electronic mail traffic. Commun ACM 36: 78–89CrossRefGoogle Scholar
  28. Siganos G, Faloutsos M, Faloutsos P, Faloutsos C (2003) Power laws and the AS—level internet topologyGoogle Scholar
  29. Tsourakakis CE (2008) Fast counting of triangles in large real networks without counting: algorithms and laws. In: ICDMGoogle Scholar
  30. Wang M, Madhyastha T, Chan NH, Papadimitriou S, Faloutsos C (2002) Data mining meets performance evaluation: fast algorithms for modeling bursty traffic. In: ICDE, pp 507–516Google Scholar
  31. Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature 393(6684): 440–442CrossRefGoogle Scholar
  32. Young SJ, Scheinerman ER (2007) Random dot product graph models for social networks. In: WAW, pp 138–149Google Scholar
  33. Zipf GK (1932) Selective studies and the principle of relative frequency in language. Harvard University PressGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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