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Optimal navigation for characterizing the role of the nodes in complex networks


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  • Cajueiro, Daniel O.


In this paper, we explore how the approach of optimal navigation (Cajueiro (2009) [33]) can be used to evaluate the centrality of a node and to characterize its role in a network. Using the subway network of Boston and the London rapid transit rail as proxies for complex networks, we show that the centrality measures inherited from the approach of optimal navigation may be considered if one desires to evaluate the centrality of the nodes using other pieces of information beyond the geometric properties of the network. Furthermore, evaluating the correlations between these inherited measures and classical measures of centralities such as the degree of a node and the characteristic path length of a node, we have found two classes of results. While for the London rapid transit rail, these inherited measures can be easily explained by these classical measures of centrality, for the Boston underground transportation system we have found nontrivial results.

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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 389 (2010)
Issue (Month): 9 ()
Pages: 1945-1954

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Handle: RePEc:eee:phsmap:v:389:y:2010:i:9:p:1945-1954

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Keywords: Centrality measures; Complex networks; Dynamic programming; Navigation;


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  1. Tadić, Bosiljka & Thurner, Stefan, 2005. "Search and topology aspects in transport on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 183-190.
  2. Jackson, Matthew O. & Rogers, Brian W., 2005. "The economics of small worlds," Working Papers 1214, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. B. Tadić, 2001. "Adaptive random walks on the class of Web graphs," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 23(2), pages 221-228, September.
  4. Cajueiro, Daniel O. & Tabak, Benjamin M., 2008. "The role of banks in the Brazilian interbank market: Does bank type matter?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6825-6836.
  5. Zhou, Tao, 2008. "Mixing navigation on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 3025-3032.
  6. Iori, G. & Reno, R. & de Masi, G. & Caldarelli, G., 2006. "Trading strategies in the Italian interbank market," Working Papers 06/03, Department of Economics, City University London.
  7. E. P. Borges & D. O. Cajueiro & R. F.S. Andrade, 2007. "Mapping dynamical systems onto complex networks," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 58(4), pages 469-474, 08.
  8. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer, vol. 31(4), pages 581-603, December.
  9. Latora, Vito & Marchiori, Massimo, 2002. "Is the Boston subway a small-world network?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 109-113.
  10. Porta, Sergio & Crucitti, Paolo & Latora, Vito, 2006. "The network analysis of urban streets: A dual approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 853-866.
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