On the Local Approximations of Node Centrality in Internet Router-Level Topologies

  • Panagiotis Pantazopoulos
  • Merkourios Karaliopoulos
  • Ioannis Stavrakakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8221)


In many networks with distributed operation and self-organization features, acquiring their global topological information is impractical, if feasible at all. Internet protocols drawing on node centrality indices may instead approximate them with their egocentric counterparts, computed out over the nodes’ ego-networks. Surprisingly, however, in router-level topologies the approximative power of localized ego-centered measurements has not been systematically evaluated. More importantly, it is unclear how to practically interpret any positive correlation found between the two centrality metric variants.

The paper addresses both issues using different datasets of ISP network topologies. We first assess how well the egocentric metrics approximate the original sociocentric ones, determined under perfect network-wide information. To this end we use two measures: their rank-correlation and the overlap in the top-k node lists the two centrality metrics induce. Overall, the rank-correlation is high, in the order of 0.8-0.9, and, intuitively, becomes higher as we relax the ego-network definition to include the ego’s r-hop neighborhood. On the other hand, the top-k node overlap is low, suggesting that the high rank-correlation is mainly due to nodes of lower rank. We then let the node centrality metrics drive elementary network operations, such as local search strategies. Our results suggest that, even under high rank-correlation, the locally-determined metrics can hardly be effective aliases for the global ones. The implication for protocol designers is that rank-correlation is a poor indicator for the approximability of centrality metrics.


Centrality Metrics Degree Centrality Local Approximation Network Node Social Network Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    The CAIDA UCSD Macroscopic Internet Topology Data Kit-[ITDK 2011-10],
  2. 2.
    Adamic, L.A., et al.: Search in power-law networks. Physical Review E 64(4) (September 2001)Google Scholar
  3. 3.
    Brandes, U.: A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25, 163–177 (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    Brandes, U., Pich, C.: Centrality Estimation in Large Networks. Int’l Journal of Birfucation and Chaos 17(7), 2303–2318 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Chai, W.K., He, D., Psaras, I., Pavlou, G.: Cache ”less for more” in information-centric networks. In: Bestak, R., Kencl, L., Li, L.E., Widmer, J., Yin, H. (eds.) NETWORKING 2012, Part I. LNCS, vol. 7289, pp. 27–40. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Daly, E.M., Haahr, M.: Social network analysis for information flow in disconnected delay-tolerant manets. IEEE Trans. Mob. Comput. 8(5), 606–621 (2009)CrossRefGoogle Scholar
  7. 7.
    Everett, M., Borgatti, S.P.: Ego network betweenness. Social Networks 27(1), 31–38 (2005)CrossRefGoogle Scholar
  8. 8.
    Freeman, L.C.: A set of measures of centrality based on betweenness. Sociometry 40(1), 35–41 (1977)CrossRefGoogle Scholar
  9. 9.
    Goh, K.I., et al.: Universal behavior of load distribution in scale-free networks. Phys. Rev. Lett. 87(27) (December 2001)Google Scholar
  10. 10.
    Kermarrec, A.M., et al.: Second order centrality: Distributed assessment of nodes criticity in complex networks. Comp. Com. 34 (2011)Google Scholar
  11. 11.
    Lim, Y., et al.: Online estimating the k central nodes of a network. In: IEEE Network Science Workshop (NSW 2011), pp. 118–122 (June 2011)Google Scholar
  12. 12.
    Marsden, P.: Egocentric and sociocentric measures of network centrality. Social Networks 24(4), 407–422 (2002)CrossRefGoogle Scholar
  13. 13.
    Nanda, S., Kotz, D.: Localized bridging centrality for distributed network analysis. In: IEEE ICCCN 2008, Virgin Islands (August 2008)Google Scholar
  14. 14.
    Newman, M.E.J.: The Structure and Function of Complex Networks. SIAM Review 45(2), 167–256 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Pansiot, J.J., et al.: Extracting intra-domain topology from mrinfo probing. In: Proc. PAM, Zurich, Switzerland (April 2010)Google Scholar
  16. 16.
    Pantazopoulos, P., et al.: Efficient social-aware content placement for opportunistic networks. In: IFIP/IEEE WONS, Slovenia (2010)Google Scholar
  17. 17.
    Pantazopoulos, P., et al.: Centrality-driven scalable service migration. In: 23rd Int’l Teletraffic Congress (ITC 2011), San Francisco, USA (2011)Google Scholar
  18. 18.
    Pantazopoulos, P., et al.: On the local approximations of node centrality in Internet router-level topologies. Tech. rep. (January 2013),
  19. 19.
    Spring, N.T., et al.: Measuring ISP topologies with rocketfuel. IEEE/ACM Trans. Netw. 12(1), 2–16 (2004)CrossRefGoogle Scholar
  20. 20.
    Vázquez, A., et al.: Large-scale topological and dynamical properties of the Internet. Phys. Rev. E 65(6), 066130 (2002)CrossRefGoogle Scholar
  21. 21.
    Wasserman, S., Faust, K.: Social network analysis. Cambridge Univ. Pr. (1994)Google Scholar
  22. 22.
    Wehmuth, K., Ziviani, A.: Distributed assessment of the closeness centrality ranking in complex networks. In: SIMPLEX, NY, USA (2012)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Panagiotis Pantazopoulos
    • 1
  • Merkourios Karaliopoulos
    • 1
  • Ioannis Stavrakakis
    • 1
  1. 1.Department of Informatics and TelecommunicationsNational & Kapodistrian University of AthensIlissiaGreece

Personalised recommendations