Advertisement

Vertex Importance Extension of Betweenness Centrality Algorithm

  • Jiří Hanzelka
  • Michal Běloch
  • Jan Martinovič
  • Kateřina Slaninová
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 808)

Abstract

Variety of real-life structures can be simplified by a graph. Such simplification emphasizes the structure represented by vertices connected via edges. A common method for the analysis of the vertices importance in a network is betweenness centrality. The centrality is computed using the information about the shortest paths that exist in a graph. This approach puts the importance on the edges that connect the vertices. However, not all vertices are equal. Some of them might be more important than others or have more significant influence on the behavior of the network. Therefore, we introduce the modification of the betweenness centrality algorithm that takes into account the vertex importance. This approach allows the further refinement of the betweenness centrality score to fulfill the needs of the network better. We show this idea on an example of the real traffic network. We test the performance of the algorithm on the traffic network data from the city of Bratislava, Slovakia to prove that the inclusion of the modification does not hinder the original algorithm much. We also provide a visualization of the traffic network of the city of Ostrava, the Czech Republic to show the effect of the vertex importance adjustment. The algorithm was parallelized by MPI (http://www.mpi-forum.org/) and was tested on the supercomputer Salomon (https://docs.it4i.cz/) at IT4Innovations National Supercomputing Center, the Czech Republic.

Keywords

Betweenness centrality High performance computing MPI Traffic network 

Notes

Acknowledgements

This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project ‘IT4Innovations excellence in science—LQ1602’, by the IT4Innovations infrastructure which is supported from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center—LM2015070”, and partially by ANTAREX, a project supported by the EU H2020 FET-HPC program under grant 671,623, and by grant of SGS No. SP2017/182 “Solving graph problems on spatio-temporal graphs with uncertainty using HPC”, VŠB—Technical University of Ostrava, Czech Republic.

References

  1. 1.
    Li, M., Wang, J., Chen, X., Wang, H., & Pan, Y. (2011). A local average connectivity-based method for identifying essential proteins from the network level. Computational Biology and Chemistry, 35, 143–150.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Xia, J., Sun, J., Jia, P., & Zhao, Z. (2011). Do cancer proteins really interact strongly in the human protein–protein interaction network? Computational Biology and Chemistry, 35, 121–125.CrossRefGoogle Scholar
  3. 3.
    Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C. J., Wedeen, V. J., et al. (2008). Mapping the structural core of human cerebral cortex. PLoS Biology, 6, 1479–1493.CrossRefGoogle Scholar
  4. 4.
    Everett, M. G., & Borgatti, S. P. (1999). The centrality of groups and classes. Journal of Mathematical Sociology, 23, 181–201.CrossRefGoogle Scholar
  5. 5.
    Szell, M., & Thurner, S. (2010). Measuring social dynamics in a massive multiplayer online game. Social Networks, 32, 313–329.CrossRefGoogle Scholar
  6. 6.
    Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. Cambridge, England: Cambridge University Press.CrossRefGoogle Scholar
  7. 7.
    Clifton, A., Turkheimer, E., & Oltmanns, T. F. (2009). Personality disorder in social networks: Network position as a marker of interpersonal dysfunction. Social Networks, 31, 26–32.CrossRefGoogle Scholar
  8. 8.
    Vandenberghe, R., Wang, Y., Nelissen, N., Vandenbulcke, M., Dhollander, T., Sunaert, S., et al. (2013). The associative-semantic network for words and pictures: Effective connectivity and graph analysis. Brain and Language, 127, 264–272.CrossRefGoogle Scholar
  9. 9.
    He, T., Zhao, J., Li, J. (2006). Discovering relations among named entities by detecting community structure. In PACLIC20 (pp. 42–48).Google Scholar
  10. 10.
    Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2009). The backbone of the climate network. EPL (Europhysics Letters), 87.Google Scholar
  11. 11.
    Zhang, G. Q., Wang, D., & Li, G. J. (2007). Enhancing the transmission efficiency by edge deletion in scale-free networks. Physical Review E, 76.Google Scholar
  12. 12.
    Zhou, S., & Mondragón, R. J. (2004). Accurately modeling the internet topology. Physical Review E, 70.Google Scholar
  13. 13.
    Comin, C. H., & Da Fontoura Costa, L. (2011). Identifying the starting point of a spreading process in complex networks. Physical Review E, 84.Google Scholar
  14. 14.
    Kawamoto, H., & Igarashi, A. (2012). Efficient packet routing strategy in complex networks. Physica A: Statistical Mechanics and its Applications, 391, 895–904.CrossRefGoogle Scholar
  15. 15.
    Klein, D. J. (2010). Centrality measure in graphs. Journal of Mathematical Chemistry, 47, 1209–1223.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Daganzo, C. F. (1994). The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B: Methodological, 28, 269–287.CrossRefGoogle Scholar
  17. 17.
    Wang, Y., & Papageorgiou, M. (2005). Real-time freeway traffic state estimation based on extended Kalman filter: A general approach. Transportation Research Part B: Methodological, 39, 141–167.CrossRefGoogle Scholar
  18. 18.
    Ngoduy, D. (2007). Real time multiclass traffic flow modelling-English M25 freeway case study. In 12th Conference of the Hong-Kong Society for Transportation Studies (pp. 143–152).Google Scholar
  19. 19.
    Shang, P., Li, X., & Kamae, S. (2005). Chaotic analysis of traffic time series. Chaos, Solitons & Fractals, 25, 121–128.CrossRefGoogle Scholar
  20. 20.
    Hong, W. C., Dong, Y., Zheng, F., & Lai, C. Y. (2011). Forecasting urban traffic flow by SVR with continuous ACO. Applied Mathematical Modelling, 35, 1282–1291.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Galafassi, C., & Bazzan, A. L. C. (2013). Analysis of traffic behavior in regular grid and real world networks.Google Scholar
  22. 22.
    Kazerani, A., & Winter, S. (2009). Can betweenness centrality explain traffic flow? In 12th AGILE International Conference on Geographic Information Science (pp. 1–9).Google Scholar
  23. 23.
    Gao, S., Wang, Y., Gao, Y., & Liu, Y. (2012). Understanding urban traffic flow characteristics: A rethinking of betweenness centrality. Environment and Planning B: Planning and Design.Google Scholar
  24. 24.
    Zhao, P. X., & Zhao, S. M. (2016). Understanding urban traffic flow characteristics from the network centrality perspective at different granularities. International Archives of the Photogrammetry Remote Sensing and Spatial Information Sciences, 41, 263–268.CrossRefGoogle Scholar
  25. 25.
    Piggins, A. (2012). Rationality for mortals: how people cope with uncertainty, by gerd gigerenzer. The Journal of Positive Psychology, 7, 75–76.CrossRefGoogle Scholar
  26. 26.
    Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 40, 35–41.CrossRefGoogle Scholar
  27. 27.
    Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1, 269–271.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of Mathematical Sociology.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Jiří Hanzelka
    • 1
    • 2
  • Michal Běloch
    • 1
  • Jan Martinovič
    • 1
  • Kateřina Slaninová
    • 1
  1. 1.IT4InnovationsVŠB—Technical University of OstravaOstravaCzech Republic
  2. 2.Department of Computer Science, FEECSVŠB—Technical University of OstravaOstravaCzech Republic

Personalised recommendations