Complex Networks VII pp 363-375

Part of the Studies in Computational Intelligence book series (SCI, volume 644) | Cite as

Comparative Network Analysis Using KronFit

Chapter

Abstract

Comparative network analysis is an emerging line of research that provides insights into the structure and dynamics of networks by finding similarities and discrepancies in their topologies. Unfortunately, comparing networks directly is not feasible on large scales. Existing works resort to representing networks with vectors of features extracted from their topologies and employ various distance metrics to compare between these feature vectors. In this paper, instead of relying on feature vectors to represent the studied networks, we suggest fitting a network model (such as Kronecker Graph) to encode the network structure. We present the directed fitting-distance measure, where the distance from a network \(A\) to another network \(B\) is captured by the quality of \(B\)’s fit to the model derived from \(A\). Evaluation on five classes of real networks shows that KronFit based distances perform surprisingly well.

Keywords

Complex networks Comparative analysis Generative models  Distance metrics 

References

  1. 1.
    Bebber, D.P., Hynes, J., Darrah, P.R., Boddy, L., Fricker, M.D.: Biological solutions to transport network design. Proceedings of the Royal Society of London B: Biological Sciences 274(1623), 2307–2315 (2007)CrossRefGoogle Scholar
  2. 2.
    Milo, R., et al.: Network motifs: simple building blocks of complex networks. Science 298, 824827 (2002)CrossRefGoogle Scholar
  3. 3.
    Pržulj, Natasa: Biological network comparison using graphlet degree distribution. Bioinformatics 23(2), e177–e183 (2007)CrossRefGoogle Scholar
  4. 4.
    Serrano, M.Ǎ., Bogunǎ, M., Vespignani, A.: Extracting the multiscale backbone of complex weighted networks. Proc. Nat. Acad. Sci. 106(16), 6483–6488 (2009)CrossRefGoogle Scholar
  5. 5.
    Baskerville, Kim: Paczuski, Maya: Subgraph ensembles and motif discovery using an alternative heuristic for graph isomorphism. Phys. Rev. E 74(5), 051903 (2006)CrossRefGoogle Scholar
  6. 6.
    Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P.: Mixed membership stochastic blockmodels. In: Advances in Neural Information Processing Systems, pp. 33–40 (2009)Google Scholar
  7. 7.
    Myunghwan, K., Leskovec, J.: Multiplicative attribute graph model of real-world networks. Internet Math. 8(1–2), 113–160 (2012)MathSciNetMATHGoogle Scholar
  8. 8.
    Davis, M., Liu, W., Miller, P., Hunter, R.F., Kee, F.: AGWAN: A Generative Model for Labelled, Weighted Graphs. In: New Frontiers in Mining Complex Patterns, pp. 181–200. Springer International Publishing (2014)Google Scholar
  9. 9.
    Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C., Ghahramani, Z.: Kronecker graphs: an approach to modeling networks. J. Mach. Learn. Res. 11, 985–1042 (2010)MathSciNetMATHGoogle Scholar
  10. 10.
    Neudecker, H.: A note on Kronecker matrix products and matrix equation systems. SIAM J. Appl. Math. 17(3), 603–606 (1969)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Kim, M., Leskovec, J.: The network completion problem: inferring missing nodes and edges in networks. In: SDM, pp. 47–58 (2011)Google Scholar
  12. 12.
    Newman, M.: Networks: An Introduction. Oxford University Press, Oxford (2009)Google Scholar
  13. 13.
    U. of Oregon Route Views Project. Online data and reports: http://www.routeviews.org. The CAIDA UCSD, AS Relationships Dataset (years 1997–2000). http://www.caida.org/data/active/as-relationships/
  14. 14.
    Leskovec, J., Krevl, A.: Stanford Large Network Dataset Collection, June 2014. http://snap.stanford.edu/data
  15. 15.
    MacQueen, J.: Some methods of classification and analysis of multivariate observations. In: LeCam, L.M., Neyman, J., (eds.), Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, p. 281. University of California Press, Berkeley, CA (1967)Google Scholar
  16. 16.
    Ward, Jr., J.H.: Hierarchical grouping to optimize an objective function. J. Am. Stat. Assoc. 58(301), 236–244 (1963)Google Scholar
  17. 17.
    Cover, T.M., Hart, P.E.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theory 13(1), 21–27 (1967)CrossRefMATHGoogle Scholar
  18. 18.
    Halkidi, M., Batistakis, Y., Vazirgiannis, M.: On clustering validation techniques. J. Intell. Inf. Syst. 17, 107–145 (2001)CrossRefMATHGoogle Scholar
  19. 19.
    Calinski, T., Harabasz, J.: A Dendrite method for cluster analysis. Commun. Stat. 3, 1–27 (1974)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Hennig, C., Liao, T.: How to find an appropriate clustering for mixed-type variables with application to socio-economic stratification. J. Roy. Stat. Soc. Ser. C. Appl. Stat. 62, 309–369 (2013)MathSciNetGoogle Scholar
  21. 21.
    Tibshirani, R., Walter, G.: Cluster validation by prediction strength. J. Comput. Graph. Stat. 14(3), 511528 (2005)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Gordon, A.D.: Classification, 2nd edn. Chapman & Hall/CRC, Boca Raton, FL (1999)MATHGoogle Scholar
  23. 23.
    Fowlkes, E.B., Mallows, C.L.: A method for comparing two hierarchical clusterings. J. Am. Stat. Assoc. 78, 553569 (1983)MATHGoogle Scholar
  24. 24.
    Onnela, J.-P., et al.: Taxonomies of networks from community structure. Phys. Rev. E 86(3), 036104 (2012)CrossRefGoogle Scholar
  25. 25.
    Gallos, L.K., Fefferman, N.H.: Revealing effective classifiers through network comparison. EPL (Europhys. Lett.) 108(3), 38001 (2014)Google Scholar
  26. 26.
    Aliakbary, S., Motallebi, S., Rashidian, S., Habibi, J., Movaghar, A.: Distance metric learning for complex networks: towards size-independent comparison of network structures. Chaos: An Interdisciplinary. J. Nonlinear Sci. 25(2), 023111 (2015)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Information Systems EngineeringBen Gurion University of the NegevBeershebaIsrael

Personalised recommendations