Skip to main content
SpringerLink
Log in

On the rich-club effect in dense and weighted networks

  • Interdisciplinary Physics
  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a real-world network it is therefore crucial to compare the measured results with a null model counterpart. Here we focus on dense and weighted networks, proposing a suitable null model and studying the behaviour of the degree correlations as measured by the rich-club coefficient. Our method solves an existing problem with the randomization of dense unweighted graphs, and at the same time represents a generalization of the rich-club coefficient to weighted networks which is complementary to other recently proposed ones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • G. Caldarelli, Scale-Free Networks (Oxford University Press, Oxford, 2007)

  • M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    Google Scholar 

  • D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)

    Google Scholar 

  • R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2001)

    Google Scholar 

  • G. Caldarelli, R. Marchetti, L. Pietronero, Europhys. Lett. 52, 386 (2000)

    Google Scholar 

  • R. Albert, H. Jeong, A.-L. Barabási., Nature 401, 130 (1999)

    Google Scholar 

  • D. Garlaschelli, G. Caldarelli, L. Pietronero, Nature 423, 165 (2003)

    Google Scholar 

  • S. Zhou, R.J. Mondragon, IEEE Comm. Lett. 8, 180 (2004)

    Google Scholar 

  • V. Colizza, A. Flammini, M.-Á. Serrano, A. Vespignani, Nature Phys. 2, 110 (2006)

    Google Scholar 

  • S. Maslov, K. Sneppen, Science 296, 910 (2002)

    Google Scholar 

  • S. Maslov, K. Sneppen, A. Zaliznyak, Physica A 333, 529 (2004)

    Google Scholar 

  • M.-Á. Serrano, M. Boguñá, Phys. Rev. E 68, 015101 (2003)

    Google Scholar 

  • D. Garlaschelli, M.I. Loffredo, Phys. Rev. Lett. 93, 188701 (2004)

    Google Scholar 

  • K. Bhattacharya, G. Mukherjee, J. Saramaki, K. Kaski, S.S. Manna, J. Stat. Mech, P02002 (2008)

  • M.-Á. Serrano, e-print arXiv:0802.3122v1

  • T. Opsahl, V. Colizza, P. Panzarasa, J.J. Ramasco, e-print arXiv:0804.0417v1

  • M. Granovetter, Sociol. Theory 1, 201 (1983)

  • M.E.J. Newman, Phys. Rev. E 70, 056131 (2004)

    Google Scholar 

  • D. Garlaschelli, M.I. Loffredo (to appear in Phys. Rev. Lett.), e-print arXiv:0807.0927v1

  • R. Guimerá, M. Sales-Pardo, L.A.N. Amaral, Nat. Phys. 3, 63 (2007)

    Google Scholar 

  • E.N. Gilbert, Ann. Math. Stat. 30, 1144 (1959)

    Google Scholar 

  • P. Erdős, A. Rényi, Publicationes Mathematicae Debrecen 6, 290 (1959)

    Google Scholar 

  • K.S. Gleditsch, J. Confl. Resolut. 46, 712 (2002)

    Google Scholar 

  • C.A. Hidalgo, B. Klinger, A.-L. Barabási, R. Hausmann, Science 317, 482 (2007)

    Google Scholar 

  • A. Barrat, M. Barthélemy, R. Pastor-Satorras, A. Vespignani, Proc. Nat. Acad. Sci. USA 101, 3747 (2004)

    Google Scholar 

  • M.A. Serrano, M. Boguna, AIP Conf. Proc. 776, 101 (2005)

    Google Scholar 

  • M.-Á. Serrano, M. Boguñá, R. Pastor-Satorras, Phys. Rev. E 74, 055101(R) (2006)

Download references

Author information

Authors and Affiliations

  1. INFM-CNR Centro SMC and Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Moro 5, 00185, Roma, Italy

    V. Zlatic & G. Caldarelli

  2. Theoretical Physics Division, Rudjer Bošković Institute, P.O. Box 180, 10002, Zagreb, Croatia

    V. Zlatic

  3. The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014, Trieste, Italy

    G. Bianconi

  4. Dept. de Física Fonamental, Facultat de Física, Universitat de Barcelona Diagonal 647, 08028, Barcelona, Spain

    A. Díaz-Guilera & G. Caldarelli

  5. Dipartimento di Fisica, Università di Siena, Via Roma 56, 53100, Siena, Italy

    D. Garlaschelli

  6. Centro Studi e Museo della Fisica Enrico Fermi, Compendio Viminale, 00185, Roma, Italy

    F. Rao

  7. Université “Louis Pasteur” Laboratoire de Chimie Biophysique/ISIS 8, allee Gaspard Monge, 67000, Strasbourg, France

    F. Rao

  8. Linkalab, Center for the Study of Complex Networks, 09100 Cagliari, Sardegna, Italy

    G. Caldarelli

Authors
  1. V. Zlatic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Bianconi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Díaz-Guilera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Garlaschelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. F. Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. G. Caldarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Garlaschelli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zlatic, V., Bianconi, G., Díaz-Guilera, A. et al. On the rich-club effect in dense and weighted networks. Eur. Phys. J. B 67, 271–275 (2009). https://doi.org/10.1140/epjb/e2009-00007-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2009-00007-9

PACS

Search

Navigation