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Multidimensional networks: foundations of structural analysis

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Abstract

Complex networks have been receiving increasing attention by the scientific community, thanks also to the increasing availability of real-world network data. So far, network analysis has focused on the characterization and measurement of local and global properties of graphs, such as diameter, degree distribution, centrality, and so on. In the last years, the multidimensional nature of many real world networks has been pointed out, i.e. many networks containing multiple connections between any pair of nodes have been analyzed. Despite the importance of analyzing this kind of networks was recognized by previous works, a complete framework for multidimensional network analysis is still missing. Such a framework would enable the analysts to study different phenomena, that can be either the generalization to the multidimensional setting of what happens in monodimensional networks, or a new class of phenomena induced by the additional degree of complexity that multidimensionality provides in real networks. The aim of this paper is then to give the basis for multidimensional network analysis: we present a solid repertoire of basic concepts and analytical measures, which take into account the general structure of multidimensional networks. We tested our framework on different real world multidimensional networks, showing the validity and the meaningfulness of the measures introduced, that are able to extract important and non-random information about complex phenomena in such networks.

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References

  1. Abello, J., Buchsbaum, A.L., Westbrook, J.R.: A functional approach to external graph algorithms. In: Algorithmica, pp. 332–343. Springer (1998)

  2. Adamic, L.A., Lukose, R.M., Puniyani, A.R., Huberman, B.A.: Search in power-law networks. Phys. Rev. E 64(46135) (2001)

  3. Aiello, W., Chung, F., Lu, L.: A random graph model for massive graphs. In: STOC, pp. 171–180. ACM (2000)

  4. Angelova, R., Kasneci, G., Weikum, G.: Graffiti: graph-based classification in heterogeneous networks. World Wide Web 15, 139–170 (2012). doi:10.1007/s11280-011-0126-4

    Article  Google Scholar 

  5. Barabási, A.L.: Linked: The New Science of Networks. Perseus Books Group (2002)

  6. Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509 (1999)

    Article  MathSciNet  Google Scholar 

  7. Benevenuto, F., Rodrigues, T., Cha, M., Almeida, V.A.F.: Characterizing user behavior in online social networks. In: Internet Measurement Conference, pp. 49–62 (2009)

  8. Berlingerio, M., Coscia, M., Giannotti, F.: Mining the temporal dimension of the information propagation. In: IDA, pp. 237–248 (2009)

  9. Berlingerio, M., Coscia, M., Giannotti, F.: Finding and characterizing communities in multidimensional networks. In: ASONAM, pp. 490–494 (2011)

  10. Berlingerio, M., Coscia, M., Giannotti, F., Monreale, A., Pedreschi, D.: Foundations of multidimensional network analysis. In: ASONAM, pp. 485–489 (2011)

  11. Berlingerio, M., Coscia, M., Giannotti, F., Monreale, A., Pedreschi, D.: The pursuit of hubbiness: analysis of hubs in large multidimensional networks. J. Comput. Sci. 2, 223–237 (2012)

    Article  Google Scholar 

  12. Berlingerio, M., Pinelli, F., Nanni, M., Giannotti, F.: Temporal mining for interactive workflow data analysis. In: KDD pp. 109–118 (2009)

  13. Bringmann, B., Berlingerio, M., Bonchi, F., Gionis, A.: Learning and predicting the evolution of social networks. IEEE Intell. Syst. 25, 26–35 (2010)

    Article  Google Scholar 

  14. Musial, K., Kazienko, P.: Social networks on the internet. World Wide Web J. (2012). doi:10.1007/s11280-011-0155-z

  15. Buchanan, M.: Nexus: Small Worlds and the Groundbreaking Theory of Networks. W.W. Norton & Co. (2003)

  16. De Castro, R., Grossman, J.W.: Famous trails to Paul Erds. Math. Intell. 21, 51–63 (1999)

    Article  MATH  Google Scholar 

  17. Chakrabarti, D., Faloutsos, C.: Graph mining: laws, generators, and algorithms. ACM Comput. Surv. 38 (2006)

  18. Chakrabarti, D., Zhan, Y., Faloutsos, C.: R-mat: a recursive model for graph mining. In: ICDM (2004)

  19. Chen, C., Yan, X., Zhu, F., Han, J., Yu, P.S.: Graph olap: towards online analytical processing on graphs. In: ICDM, pp. 103–112 (2008)

  20. Cook, D.J., Crandall, A.S., Singla, G., Thomas, B.: Detection of social interaction in smart spaces. Cybern. Syst. 41(2), 90–104 (2010)

    Article  MATH  Google Scholar 

  21. Donato, D.: Graph structures and algorithms for query-log analysis. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds.) CiE, Lecture Notes in Computer Science, vol. 6158, pp. 126–131. Springer (2010)

  22. Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. In: SIGCOMM, pp. 251–262 (1999)

  23. Gomez-Rodriguez, M., Leskovec, J., Krause, A.: Inferring networks of diffusion and influence. In: KDD, pp. 1019–1028 (2010)

  24. Jeong, H., Mason, S.P., Barabasi, A.L., Oltvai, Z.N.: Lethality and centrality in protein networks. Nature 411(6833), 41–42 (2001)

    Article  Google Scholar 

  25. Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabási, A.L.: The large-scale organization of metabolic networks. Nature 407(6804), 651–654 (2000)

    Article  Google Scholar 

  26. Kashima, H., Kato, T., Yamanishi, Y., Sugiyama, M., Tsuda, K.: Link propagation: a fast semi-supervised learning algorithm for link prediction. In: SDM, pp. 1099–1110. SIAM (2009)

  27. Kleinberg, J.M., Kumar, R., Raghavan, P., Rajagopalan, S., Tomkins, A.S.: The Web as a Graph: Measurements, Models, and Methods (1999)

  28. Leskovec, J., Huttenlocher, D., Kleinberg, J.: Predicting positive and negative links in online social networks. In: WWW, pp. 641–650. ACM (2010)

  29. Mucha, P.J., Richardson, T., Macon, K., Porter, M.A., Onnela, J.-P.: Community structure in time-dependent, multiscale, and multiplex networks. Science 328, 876 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  30. Newman, M.E.J.: The Structure and Function of Complex Networks (2003)

  31. Nowell, D.L., Kleinberg, J.: The link prediction problem for social networks. In: CIKM ’03, pp. 556–559. ACM (2003)

  32. Pass, G., Chowdhury, A., Torgeson, C.: A picture of search. In: InfoScale ’06, p. 1. ACM (2006)

  33. Redner, S.: How popular is your paper? an empirical study of the citation distribution. Eur. Phys. J., B Cond. Matter Complex Syst. 4(2), 131–134 (1998)

    Article  Google Scholar 

  34. Rossetti, G., Berlingerio, M., Giannotti, F.: Scalable link prediction on multidimensional networks. In: Spiliopoulou, M., Wang, H., Cook, D.J., Pei, J., Wang, W., Zaïane, O.R., Wu, X. (eds.) ICDM Workshops, pp, 979–986. IEEE (2011)

  35. Szell, M., Lambiotte, R., Thurner, S.: Trade, conflict and sentiments: multi-relational organization of large-scale social networks. PNAS 107(31), 13636–13641. arXiv.1003.5137 (2010)

    Google Scholar 

  36. Tang, L., Liu, H.: Relational learning via latent social dimensions. In: KDD, pp. 817–826. ACM (2009)

  37. Watts, D.J.: Six Degrees: The Science of a Connected Age (2003)

  38. Yan, X., Han, J.: gspan: graph-based substructure pattern mining. ICDM ’02, pp. 721–724 (2002)

  39. Yang, J., Leskovec, J.: Modeling information diffusion in implicit networks. In: Webb, G.I., Liu, B., Zhang, C., Gunopulos, D., Wu, X. (eds.) ICDM, pp. 599–608. IEEE Computer Society (2010)

  40. Zhao, P., Yu., J.: Fast frequent free tree mining in graph databases. World Wide Web 11, 71–92 (2008). doi:10.1007/s11280-007-0031-z

    Article  Google Scholar 

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Authors and Affiliations

  1. IBM Research, IBM Technology Campus, Damastown Industrial Estate, Dublin 15, Ireland

    Michele Berlingerio

  2. Center for International Development, Harvard University, 79 JFK St, 02138, Cambridge, MA, USA

    Michele Coscia

  3. KDDLab, ISTI - CNR, via G. Moruzzi 1, 56124, Pisa, Italy

    Fosca Giannotti

  4. KDDLab, Dept. of Computer Science, University of Pisa, largo B. Pontecorvo 3, 56100, Pisa, Italy

    Anna Monreale & Dino Pedreschi

Authors
  1. Michele Berlingerio
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  2. Michele Coscia
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  3. Fosca Giannotti
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  4. Anna Monreale
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  5. Dino Pedreschi
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Corresponding author

Correspondence to Michele Berlingerio.

Additional information

This work was done when Michele Berlingerio and Michele Coscia were with KDDLab, ISTI - CNR, Pisa, Italy

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Berlingerio, M., Coscia, M., Giannotti, F. et al. Multidimensional networks: foundations of structural analysis. World Wide Web 16, 567–593 (2013). https://doi.org/10.1007/s11280-012-0190-4

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  • DOI: https://doi.org/10.1007/s11280-012-0190-4

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