Communicability and Communities in Complex Socio-Economic Networks


The concept of communicability is introduced for complex socio-economic networks. The communicability function expresses how an impact propagates from one place to another in the network. This function is used to define unambiguously the concept of socio-economic community. The concept of temperature in complex socio-economic networks is also introduced as a way of accounting for the external stresses to which such systems are submitted. This external stress can change dramatically the structure of the communities in a network. We analyze here a trade network of countries exporting ‘miscellaneous manufactures of metal.’ We determine the community structure of this network showing that there are 27 communities with diverse degree of overlapping. When only communities with less than 80% of overlap are considered we found five communities which are well characterized in terms of geopolitical relationships. The analysis of external stress on these communities reveals the vulnerability of the trade network in critical situations, i.e., economical crisis. The current approach adds an important tool for the analysis of socio-economic networks in the real world.


Adjacency Matrix External Stress Communicability Function Communicability Graph Trade Network 
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.



EE thanks B. Álvarez-Pereira and K. Deegan for help with the calculations. EE also thanks partial financial support from the New Professor’s Fund given by the Principal, University of Strathclyde.


  1. 1.
    Jackson MO (2008) Social and economic networks. Princeton University Press, PrincetonMATHGoogle Scholar
  2. 2.
    Souma W, Fujiwara Y, Aoyama H (2003) Physica A 324:396–401MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Asmin S (1997) Capitalism in the age of globalization: the management of contemporary society. Zed Books, LondonGoogle Scholar
  4. 4.
    Serrano MA, Boguñá M (2003) Phys Rev E 68:015101ADSCrossRefGoogle Scholar
  5. 5.
    Newman MJE (2003) SIAM Rev 45:167–256MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Estrada E, Hatano N (2008) Phys Rev E 77:036111MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Cvetković D, Rowlinson P, Simić S (1997) Eigenspaces of graphs. Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  8. 8.
    Estrada E, Hatano N (2009) Appl Math Comput 214:500–511MATHCrossRefGoogle Scholar
  9. 9.
    Sørensen T (1948) Biol Skr 5:1–34Google Scholar
  10. 10.
    Estrada E, Hatano N (2007) Chem Phys Let 439:247–251ADSCrossRefGoogle Scholar
  11. 11.
    Zachary WW (1977) J Anthropol Res 33:452–473Google Scholar
  12. 12.
    de Nooy W, Mrvar A, Batagelj V (2005) Exploratory social network analysis with Pajek. Cambridge University Press, CambridgeCrossRefGoogle Scholar

Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Department of Physics and Institute of Complex SystemsUniversity of StrathclydeGlasgowUK
  2. 2.Institute of Industrial ScienceThe University of TokyoMeguro-kuJapan

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