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Towards a Systematic Evaluation of Generative Network Models

  • Thomas Bläsius
  • Tobias Friedrich
  • Maximilian KatzmannEmail author
  • Anton Krohmer
  • Jonathan Striebel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10836)

Abstract

Generative graph models play an important role in network science. Unlike real-world networks, they are accessible for mathematical analysis and the number of available networks is not limited. The explanatory power of results on generative models, however, heavily depends on how realistic they are. We present a framework that allows for a systematic evaluation of generative network models. It is based on the question whether real-world networks can be distinguished from generated graphs with respect to certain graph parameters.

As a proof of concept, we apply our framework to four popular random graph models (Erdős-Rényi, Barabási-Albert, Chung-Lu, and hyperbolic random graphs). Our experiments for example show that all four models are bad representations for Facebook’s social networks, while Chung-Lu and hyperbolic random graphs are good representations for other networks, with different strengths and weaknesses.

Keywords

Generative graph models Real-world comparison Distinguishability of network classes 

Notes

Acknowledgements

This research has received funding from the German Research Foundation (DFG) under grant agreement no. FR 2988 (ADLON, HYP).

References

  1. 1.
    Attar, N., Aliakbary, S.: Classification of complex networks based on similarity of topological network features. Chaos 27(9), 1–7 (2017)CrossRefGoogle Scholar
  2. 2.
    Baldi, P., Brunak, S., Chauvin, Y., Andersen, C.A.F., Nielsen, H.: Assessing the accuracy of prediction algorithms for classification: an overview. Bioinformatics 16(5), 412–424 (2000)CrossRefGoogle Scholar
  3. 3.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bennett, K.P., Campbell, C.: Support vector machines: hype or hallelujah? SIGKDD Explor. 2(2), 1–13 (2000)CrossRefGoogle Scholar
  5. 5.
    Bläsius, T., Friedrich, T., Krohmer, A., Laue, S.: Efficient embedding of scale-free graphs in the hyperbolic plane. In: 24th ESA, pp. 16:1–16:18 (2016)Google Scholar
  6. 6.
    Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24(1), 5–34 (2004)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random Struct. Algor. 18(3), 279–290 (2001)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Chung, F., Lu, L.: The average distances in random graphs with given expected degrees. Proc. Natl. Acad. Sci. 99(25), 15879–15882 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Chung, F., Lu, L.: Connected components in random graphs with given expected degree sequences. Ann. Comb. 6(2), 125–145 (2002)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Easley, D., Kleinberg, J.: The small-world phenomenon. In: Networks, Crowds, and Markets: Reasoning About a Highly Connected World, Chap. 20, pp. 611–644. Cambridge University Press (2010)Google Scholar
  11. 11.
    Eggemann, N., Noble, S.D.: The clustering coefficient of a scale-free random graph. Discrete Appl. Math. 159(10), 953–965 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Erdős, P., Rényi, A.: On random graphs I. Publ. Math. 6, 290–297 (1959)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Fernández-Delgado, M., Cernadas, E., Barro, S., Amorim, D., Amorim Fernández-Delgado, D.: Do we need hundreds of classifiers to solve real world classification problems? J. Mach. Learn. Res. 15, 3133–3181 (2014)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Friedrich, T., Krohmer, A.: On the diameter of hyperbolic random graphs. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 614–625. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-47666-6_49CrossRefGoogle Scholar
  15. 15.
    Gugelmann, L., Panagiotou, K., Peter, U.: Random hyperbolic graphs: degree sequence and clustering. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 573–585. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31585-5_51CrossRefzbMATHGoogle Scholar
  16. 16.
    Karp, R.M.: The probabilistic analysis of combinatorial optimization algorithms. In: Proceedings of the International Congress of Mathematicians, pp. 1601–1609 (1983)Google Scholar
  17. 17.
    Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., Boguñá, M.: Hyperbolic geometry of complex networks. Phys. Rev. E 82(3), 036106 (2010)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (2015). http://networkrepository.com
  19. 19.
    Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.): Advances in Kernel Methods: Support Vector Learning. MIT Press, Cambridge (1999)Google Scholar
  20. 20.
    Soundarajan, S., Eliassi-Rad, T., Gallagher, B.: A guide to selecting a network similarity method. In: SDM, pp. 1037–1045 (2014)CrossRefGoogle Scholar
  21. 21.
    Staudt, C.L., Sazonovs, A., Meyerhenke, H.: NetworKit: a tool suite for large-scale complex network analysis. Netw. Sci. 4(4), 508–530 (2016)CrossRefGoogle Scholar
  22. 22.
    Watts, D.J.: A simple model of global cascades on random networks. Proc. Natl. Acad. Sci. 99(9), 5766–5771 (2002)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of “small-world” networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Thomas Bläsius
    • 1
  • Tobias Friedrich
    • 1
  • Maximilian Katzmann
    • 1
    Email author
  • Anton Krohmer
    • 1
  • Jonathan Striebel
    • 1
  1. 1.Hasso Plattner InstitutePotsdamGermany

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