Letter | Published:

Link communities reveal multiscale complexity in networks

Nature volume 466, pages 761764 (05 August 2010) | Download Citation


Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society1,2,3. One crucial step when studying the structure and dynamics of networks is to identify communities4,5: groups of related nodes that correspond to functional subunits such as protein complexes6,7 or social spheres8,9,10. Communities in networks often overlap9,10 such that nodes simultaneously belong to several groups. Meanwhile, many networks are known to possess hierarchical organization, where communities are recursively grouped into a hierarchical structure11,12,13. However, the fact that many real networks have communities with pervasive overlap, where each and every node belongs to more than one group, has the consequence that a global hierarchy of nodes cannot capture the relationships between overlapping groups. Here we reinvent communities as groups of links rather than nodes and show that this unorthodox approach successfully reconciles the antagonistic organizing principles of overlapping communities and hierarchy. In contrast to the existing literature, which has entirely focused on grouping nodes, link communities naturally incorporate overlap while revealing hierarchical organization. We find relevant link communities in many networks, including major biological networks such as protein–protein interaction6,7,14 and metabolic networks11,15,16, and show that a large social network10,17,18 contains hierarchically organized community structures spanning inner-city to regional scales while maintaining pervasive overlap. Our results imply that link communities are fundamental building blocks that reveal overlap and hierarchical organization in networks to be two aspects of the same phenomenon.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    , & The Structure and Dynamics of Networks (Princeton Univ. Press, 2006)

  2. 2.

    Scale-Free Networks: Complex Webs in Nature and Technology (Oxford Univ. Press, 2007)

  3. 3.

    , & Critical phenomena in complex networks. Rev. Mod. Phys. 80, 1275–1335 (2008)

  4. 4.

    & Community structure in social and biological networks. Proc. Natl Acad. Sci. USA 99, 7821–7826 (2002)

  5. 5.

    Community detection in graphs. Phys. Rep. 486, 75–174 (2010)

  6. 6.

    et al. Global landscape of protein complexes in the yeast Saccharomyces cerevisiae. Nature 440, 637–643 (2006)

  7. 7.

    et al. Proteome survey reveals modularity of the yeast cell machinery. Nature 440, 631–636 (2006)

  8. 8.

    & Social Network Analysis: Methods and Applications. Structural analysis in the social sciences (Cambridge Univ. Press, 1994)

  9. 9.

    , , & Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)

  10. 10.

    , & Quantifying social group evolution. Nature 446, 664–667 (2007)

  11. 11.

    , , , & Hierarchical organization of modularity in metabolic networks. Science 297, 1551–1555 (2002)

  12. 12.

    , , & Extracting the hierarchical organization of complex systems. Proc. Natl Acad. Sci. USA 104, 15224–15229 (2007)

  13. 13.

    , & Hierarchical structure and the prediction of missing links in networks. Nature 453, 98–101 (2008)

  14. 14.

    et al. High-quality binary protein interaction map of the yeast interactome network. Science 322, 104–110 (2008)

  15. 15.

    & Functional cartography of complex metabolic networks. Nature 433, 895–900 (2005)

  16. 16.

    et al. A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 orfs and thermodynamic information. Mol. Syst. Biol. 3, 121 (2007)

  17. 17.

    et al. Structure and tie strengths in mobile communication networks. Proc. Natl Acad. Sci. USA 104, 7332–7336 (2007)

  18. 18.

    , & Understanding individual human mobility patterns. Nature 453, 779–782 (2008)

  19. 19.

    , , , & Defining and identifying communities in networks. Proc. Natl Acad. Sci. USA 101, 2658–2663 (2004)

  20. 20.

    & Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)

  21. 21.

    & Maps of random walks on complex networks reveal community structure. Proc. Natl Acad. Sci. USA 105, 1118–1123 (2008)

  22. 22.

    & Detecting fuzzy community structures in complex networks with a Potts model. Phys. Rev. Lett. 93, 218701 (2004)

  23. 23.

    et al. Synchronization interfaces and overlapping communities in complex networks. Phys. Rev. Lett. 101, 168701 (2008)

  24. 24.

    , & Detecting the overlapping and hierarchical community structure in complex networks. N. J. Phys. 11, 033015 (2009)

  25. 25.

    & Resolution limit in community detection. Proc. Natl Acad. Sci. USA 104, 36–41 (2007)

  26. 26.

    , & Finding community structure in very large networks. Phys. Rev. E 70, 066111 (2004)

  27. 27.

    & Community detection algorithms: a comparative analysis. Phys. Rev. E 80, 056117 (2009)

  28. 28.

    The Gene Ontology Consortium. The Gene Ontology project in 2008. Nucleic Acids Res. 36, D440–D444 (2008)

  29. 29.

    & Line graphs, link partitions and overlapping communities. Phys. Rev. E 80, 016105 (2009)

  30. 30.

    & Edge partitions and overlapping communities in complex networks. Preprint at 〈〉 (2009)

Download references


The authors thank A.-L. Barabási, S. Ahnert, J. Park, D.-S. Lee, P.-J. Kim, N. Blumm, D. Wang, M. A. Yildirim and H. Yu. The authors acknowledge the Center for Complex Network Research, supported by the James S. McDonnell Foundation 21st Century Initiative in Studying Complex Systems; the NSF-DDDAS (CNS-0540348), NSF-ITR (DMR-0426737) and NSF-IIS-0513650 programmes; US ONR Award N00014-07-C; the NIH (U01 A1070499-01/Sub #:111620-2); the DTRA (BRBAA07-J-2-0035); the NS-CTA sponsored by US ARL (W911NF-09-2-0053); and NKTH NAP (KCKHA005). S.L. acknowledges support from the Danish Natural Science Research Council.

Author information

Author notes

    • Yong-Yeol Ahn
    • , James P. Bagrow
    •  & Sune Lehmann

    These authors contributed equally to this work.


  1. Center for Complex Network Research, Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

    • Yong-Yeol Ahn
    •  & James P. Bagrow
  2. Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Harvard University, Boston, Massachusetts 02215, USA

    • Yong-Yeol Ahn
    •  & James P. Bagrow
  3. Institute for Quantitative Social Science, Harvard University, Cambridge, Massachusetts 02138, USA

    • Sune Lehmann
  4. College of Computer and Information Science, Northeastern University, Boston, Massachusetts 02115, USA

    • Sune Lehmann


  1. Search for Yong-Yeol Ahn in:

  2. Search for James P. Bagrow in:

  3. Search for Sune Lehmann in:


Y.-Y.A., J.P.B. and S.L. designed and performed the research and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Sune Lehmann.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains a Supplementary Information (see Table of Contents), Supplementary Figures S1-S32 with legends, Supplementary Tables S1-S2 and References.

Zip files

  1. 1.

    Supplementary Table 1

    This file contains the details for PPI link communities.

  2. 2.

    Supplementary Table 2

    This file contains the details for metabolic link communities.

  3. 3.

    Supplementary Table 3

    This file contains the details for word association link communities.

About this article

Publication history






Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.