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The organization of strong links in complex networks

Nature Physics volume 8, pages 429–436 (2012)Cite this article

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Abstract

Many complex systems reveal a small-world topology, which allows simultaneously local and global efficiency in the interaction between system constituents. Here, we report the results of a comprehensive study that investigates the relation between the clustering properties in such small-world systems and the strength of interactions between its constituents, quantified by the link weight. For brain, gene, social and language networks, we find a local integrative weight organization in which strong links preferentially occur between nodes with overlapping neighbourhoods; we relate this to global robustness of the clustering to removal of the weakest links. Furthermore, we identify local learning rules that establish integrative networks and improve network traffic in response to past traffic failures. Our findings identify a general organization for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions.

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Figure 1: Link clustering in real-world networks reveals preferential placement of strong links with respect to the neighbourhood overlap of the corresponding end nodes.
Figure 2: The robustness of clustering to the loss of their weakest or strongest links in small-world networks and its correlation to link clustering.
Figure 3: Link clustering and pruning analysis for neutral, dispersive, and integrative weight organizations.
Figure 4: Summary plot of M versus R C L for all the networks analysed in the present study.
Figure 5: The cohesive nature of weak links is grounded in their random organization.
Figure 6: Adaptive implementation of integrative and dispersive weight organization.

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Acknowledgements

We thank M. Boguna and members of the Section on Critical Brain Dynamics, NIMH, NIH, for constructive comments during this work. We also thank S. Yu for providing some of the monkey data and J. Alstott for Matlab implementation of one of the social network models. This work was supported by the NIH Intramural Research Program of the NIMH and the DCB/CIT.

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Authors and Affiliations

  1. Division of Computational Bioscience, Mathematical and Statistical Computing Laboratory, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA

    Sinisa Pajevic

  2. Section on Critical Brain Dynamics, Laboratory of Systems Neuroscience, National Institute of Mental Health, Bethesda, Maryland 20892, USA

    Dietmar Plenz

Authors
  1. Sinisa Pajevic
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  2. Dietmar Plenz
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Contributions

S.P. did analysis. S.P. and D.P. discussed, commented upon and wrote the manuscript.

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Correspondence to Sinisa Pajevic.

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The authors declare no competing financial interests.

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Pajevic, S., Plenz, D. The organization of strong links in complex networks. Nature Phys 8, 429–436 (2012). https://doi.org/10.1038/nphys2257

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