RTG: A Recursive Realistic Graph Generator Using Random Typing

  • Leman Akoglu
  • Christos Faloutsos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5781)


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 27K nodes and 125K edges; and Committee-to-Candidate campaign donations (bipartite, directed, weighted) with 23K nodes and 880K edges. We also show how to handle time so that edge/weight additions are bursty and self-similar.


Degree Distribution Graph Generator Output Graph Campaign Donation Unique Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Akoglu, L., McGlohon, M., Faloutsos, C.: Rtm: Laws and a recursive generator for weighted time-evolving graphs. In: ICDM (2008)Google Scholar
  2. 2.
    Albert, R., Jeong, H., Barabasi, A.-L.: Diameter of the World Wide Web. Nature 401, 130–131 (1999)CrossRefGoogle Scholar
  3. 3.
    Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chakrabarti, D., Faloutsos, C.: Graph mining: Laws, generators, and algorithms. ACM Comput. Surv. 38(1) (2006)Google Scholar
  5. 5.
    Chakrabarti, D., Zhan, Y., Faloutsos, C.: R-MAT: A recursive model for graph mining. In: SIAM Int. Conf. on Data Mining (April 2004)Google Scholar
  6. 6.
    Conrad, B., Mitzenmacher, M.: Power laws for monkeys typing randomly: the case of unequal probabilities. IEEE Transactions on Information Theory 50(7), 1403–1414 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Crovella, M., Bestavros, A.: Self-similarity in world wide web traffic, evidence and possible causes. Sigmetrics, 160–169 (1996)Google Scholar
  8. 8.
    Erdos, P., Renyi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungary. Acad. Sci. 5, 17–61 (1960)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Even-Bar, E., Kearns, M., Suri, S.: A network formation game for bipartite exchange economies. In: SODA (2007)Google Scholar
  10. 10.
    Fabrikant, A., Luthra, A., Maneva, E.N., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: PODC (2003)Google Scholar
  11. 11.
    Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. In: SIGCOMM, August-September 1999, pp. 251–262 (1999)Google Scholar
  12. 12.
    Flake, G.W., Lawrence, S., Giles, C.L., Coetzee, F.M.: Self-organization and identification of web communities. IEEE Computer 35, 66–71 (2002)CrossRefGoogle Scholar
  13. 13.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. PNAS 99, 7821 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gomez, M.E., Santonja, V.: Self-similarity in i/o workload: Analysis and modeling. In: WWC (1998)Google Scholar
  15. 15.
    Gribble, S.D., Manku, G.S., Roselli, D., Brewer, E.A., Gibson, T.J., Miller, E.L.: Self-similarity in file systems. In: SIGMETRICS 1998 (1998)Google Scholar
  16. 16.
    Kleinberg, J.M., Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.S.: The Web as a graph: Measurements, models and methods. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol. 1627, pp. 1–17. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  17. 17.
    Scheinerman, E., Kraetzl, M., Nickel, C.: Random dot product graphs: a model for social networks (Preliminary Manuscript) (2005)Google Scholar
  18. 18.
    Laoutaris, N., Poplawski, L.J., Rajaraman, R., Sundaram, R., Teng, S.-H.: Bounded budget connection (bbc) games or how to make friends and influence people, on a budget. In: PODC (2008)Google Scholar
  19. 19.
    Leskovec, J., Chakrabarti, D., Kleinberg, J.M., Faloutsos, C.: Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication. In: Jorge, A.M., Torgo, L., Brazdil, P.B., Camacho, R., Gama, J. (eds.) PKDD 2005. LNCS (LNAI), vol. 3721, pp. 133–145. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: ACM SIGKDD (2005)Google Scholar
  21. 21.
    Mandelbrot, B.: An informational theory of the statistical structure of language. Communication Theory (1953)Google Scholar
  22. 22.
    McGlohon, M., Akoglu, L., Faloutsos, C.: Weighted graphs and disconnected components: Patterns and a generator. In: ACM SIGKDD, Las Vegas (August 2008)Google Scholar
  23. 23.
    Miller, G.A.: Some effects of intermittent silence. American Journal of Psychology 70, 311–314 (1957)CrossRefGoogle Scholar
  24. 24.
    Newman, M.E.J.: Power laws, Pareto distributions and Zipf’s law (December 2004)Google Scholar
  25. 25.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E 69, 026113 (2004)CrossRefGoogle Scholar
  26. 26.
    Pennock, D.M., Flake, G.W., Lawrence, S., Glover, E.J., Giles, C.L.: Winners don’t take all: Characterizing the competition for links on the web. Proceedings of the National Academy of Sciences, 5207–5211 (2002)Google Scholar
  27. 27.
    Schwartz, M.F., Wood, D.C.M.: Discovering shared interests among people using graph analysis of global electronic mail traffic. Communications of the ACM 36, 78–89 (1992)CrossRefGoogle Scholar
  28. 28.
    Siganos, G., Faloutsos, M., Faloutsos, P., Faloutsos, C.: Power laws and the AS-level internet topology (2003)Google Scholar
  29. 29.
    Tsourakakis, C.E.: Fast counting of triangles in large real networks without counting: Algorithms and laws. In: ICDM (2008)Google Scholar
  30. 30.
    Wang, M., Madhyastha, T., Chan, N.H., Papadimitriou, S., Faloutsos, C.: Data mining meets performance evaluation: Fast algorithms for modeling bursty traffic. In: ICDE, pp. 507–516 (2002)Google Scholar
  31. 31.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393(6684), 440–442 (1998)CrossRefGoogle Scholar
  32. 32.
    Young, S.J., Scheinerman, E.R.: Random dot product graph models for social networks. In: Bonato, A., Chung, F.R.K. (eds.) WAW 2007. LNCS, vol. 4863, pp. 138–149. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  33. 33.
    Zipf, G.K.: Selective Studies and the Principle of Relative Frequency in Language. Harvard University Press (1932)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Leman Akoglu
    • 1
  • Christos Faloutsos
    • 1
  1. 1.School of Computer ScienceCarnegie Mellon UniversityUSA

Personalised recommendations