Advertisement

Stability and Similarity in Networks Based on Topology and Nodes Importance

  • Fuad Aleskerov
  • Sergey Shvydun
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)

Abstract

We propose a model that evaluates how much a network has changed over time in terms of its structure and a set of central elements. The difference of structure is evaluated in terms of node-to-node influence using known nodes correspondence models. To analyze the changes in nodes centralities we adapt an idea of interval orders to the network theory. Our approach can be used to investigate dynamic changes in temporal networks and to identify suspicious or abnormal effects in terms of the topology and its critical members. We can also transform the stability measure to the similarity measure in order to cluster the network in some homogeneous periods. To test our model, we consider the international migration network from 1970 to 2015 and attempt to analyze main changes in migration patterns.

Keywords

Network stability Similarity measure Temporal networks Topology Dynamics 

Notes

Acknowledgments

The article was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) and supported within the framework of a subsidy by the Russian Academic Excellence Project’5-100’. The empirical application to international migration network was funded by the Russian Science Foundation under grant № 17-18-01651.

References

  1. Akoglu, L., Tong, H., Koutra, D.: Graph-based anomaly detection and description: a survey (2015). arXiv preprint arXiv: 1404.4679Google Scholar
  2. Aleskerov, F., Bouyssou, D., Monjardet, B.: Utility Maximization, Choice and Preference, vol. 16. Springer Science & Business Media (2007)Google Scholar
  3. Aleskerov, F., Meshcheryakova, N., Shvydun, S.: Centrality measures in networks based on nodes attributes, long-range interactions and group influence (2016). arXiv preprint arXiv:1610.05892
  4. Aleskerov, F.T., Meshcheryakova, N.G., Rezyapova, A., Shvydun, S.V.: Network analysis of international migration. In: Kalyagin, V.A., Nikolaev, A.I., Pardalos, P.M., Prokopyev, O. (eds.) Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol. 197, pp. 177–185. Springer (2014)Google Scholar
  5. Aleskerov, F.T., Meshcheryakova, N.G., Shvydun, S.V.: Power in network structures. In: Kalyagin, V.A., Nikolaev, A.I., Pardalos, P.M., Prokopyev, O. (eds.) Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol. 197, pp. 79–85. Springer (2017)Google Scholar
  6. Aleskerov, F.T., Meshcheryakova, N.G., Rezyapova, A., Shvydun, S.V.: Network analysis of international migration (2016). arXiv preprint arXiv:1806.06705
  7. Borodin, A., Roberts, G.O., Rosenthal, J.S., Tsaparas, P.: Link analysis ranking: algorithms, theory, and experiments. ACM Trans. Internet Technol. 5(1), 231–297 (2005)Google Scholar
  8. Broder, A., Glassman, S., Manasse, M., Zweig, G.: Syntactic clustering of the web. In: WWW, pp. 393–404 (1997)Google Scholar
  9. Bunke, H., Dickinson, P.J., Kraetzl, M., Wallis, W.D.: A Graphtheoretic Approach to Enterprise Network Dynamics. Birkhäuser, Boston (2007)Google Scholar
  10. De Domenico, M., Nicosia, V., Arenas, A., Latora, V.: Structural reducibility of multilayer networks. Nat. Commun. 6, 7864 (2015)Google Scholar
  11. Johnson, S.C.: Psychometrika 32, 241 (1967)Google Scholar
  12. Koutra, D., Ke, T.Y., Kang, U., Chau, D.H., Pao, H.K.K., Faloutsos, C.: Unifying guilt-by-association approaches: theorems and fast algorithms. In: Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD), Athens, Greece (2011)Google Scholar
  13. Koutra, D., Vogelstein, J., Faloutsos, C.: Deltacon: a principled massive-graph similarity function. In: Proceedings of the 13th SIAM International Conference on Data Mining (SDM), Texas-Austin, TX (2013)Google Scholar
  14. Lakhina, A., Crovella, M., Diot, C.: Diagnosing network-wide traffic anomalies. In: Proceedings of the ACM Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (SIGCOMM’04), pp. 65–76. ACM Press, Portland, Ore, USA, Aug 2004Google Scholar
  15. Mirkin, B.: Clustering: A Data Recovery Approach, 2nd edn. Chapman and Hall/CRC (2012)Google Scholar
  16. Papadopoulos, A.N., Manolopoulos, Y.: Structure-based similarity search with graph histograms. In: Proceedings Tenth International Workshop on Database and Expert Systems Applications. DEXA 99, Florence, Italy, pp. 174–178 (1999)Google Scholar
  17. Papadimitriou, P., Dasdan, A., Garcia-Molina, H.: J. Internet Serv. Appl. 1, 19 (2010)Google Scholar
  18. Raymond, J.W., Gardiner, E.J., Willett, P.: RASCAL: calculation of graph similarity using maximum common edge subgraphs. Comput. J. 45(6), 631–644 (2002)Google Scholar
  19. United Nations, Department of Economic and Social Affairs, Population Division. International Migration Flows to and from Selected Countries: The 2015 Revision (POP/DB/MIG/Flow/Rev.2015) (2015)Google Scholar
  20. Wiener, N.: A contribution to the theory of relative position. Proc. Camb. Philos. Soc. 17, 441–449 (1914)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.V.A. Trapeznikov Institute of Control Sciences of Russian Academy of SciencesMoscowRussia

Personalised recommendations