Scaling Properties of Human Brain Functional Networks

  • Riccardo ZuccaEmail author
  • Xerxes D. Arsiwalla
  • Hoang Le
  • Mikail Rubinov
  • Paul F. M. J. Verschure
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9886)


We investigate scaling properties of human brain functional networks in the resting-state. Analyzing network degree distributions, we statistically test whether their tails scale as power-law or not. Initial studies, based on least-squares fitting, were shown to be inadequate for precise estimation of power-law distributions. Subsequently, methods based on maximum-likelihood estimators have been proposed and applied to address this question. Nevertheless, no clear consensus has emerged, mainly because results have shown substantial variability depending on the data-set used or its resolution. In this study, we work with high-resolution data (10 K nodes) from the Human Connectome Project and take into account network weights. We test for the power-law, exponential, log-normal and generalized Pareto distributions. Our results show that the statistics generally do not support a power-law, but instead these degree distributions tend towards the thin-tail limit of the generalized Pareto model. This may have implications for the number of hubs in human brain functional networks.


Power-law distributions Functional connectivity Generalized pareto Model fitting Maximum likelihood Connectome Brain networks 



The work has been supported by the European Research Council under the EUs 7th Framework Programme (FP7/2007-2013)/ERC grant agreement no. 341196 to P. Verschure. Data were provided [in part] by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University.


  1. 1.
    Achard, S., Salvador, R., Whitcher, B., Suckling, J., Bullmore, E.: A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J. Neurosci. Official J. Soc. Neurosci. 26(1), 63–72 (2006)CrossRefGoogle Scholar
  2. 2.
    Albert, R., Jeong, H., Barabási, A.L.: Error and attack tolerance of complex networks. Nature 406(6794), 378–382 (2000)CrossRefGoogle Scholar
  3. 3.
    Arsiwalla, X.D., Betella, A., Martínez, E., Omedas, P., Zucca, R., Verschure, P.: The dynamic connectome: a tool for large scale 3D reconstruction of brain activity in real time. In: Rekdalsbakken, W., Bye, R., Zhang, H., (eds.) 27th European Conference on Modeling and Simulation, ECMS, Alesund (Norway) (2013)Google Scholar
  4. 4.
    Arsiwalla, X.D., Dalmazzo, D., Zucca, R., Betella, A., Brandi, S., Martinez, E., Omedas, P., Verschure, P.: Connectomics to semantomics: addressing the brain’s big data challenge. Procedia Comput. Sci. 53, 48–55 (2015)CrossRefGoogle Scholar
  5. 5.
    Arsiwalla, X.D., Zucca, R., Betella, A., Martinez, E., Dalmazzo, D., Omedas, P., Deco, G., Verschure, P.: Network dynamics with BrainX3: a large-scale simulation of the human brain network with real-time interaction. Front. Neuroinf. 9(2) (2015)Google Scholar
  6. 6.
    Clauset, A., Shalizi, C., Newman, M.: Power-law distributions in empirical data. SIAM Rev. 51(4), 661–703 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Eguíluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V.: Scale-free brain functional networks. Phys. Rev. Lett. 94(1), 018102 (2005)CrossRefGoogle Scholar
  8. 8.
    Fornito, A., Zalesky, A., Bullmore, E.T.: Network scaling effects in graph analytic studies of human resting-state fMRI data. Front. Syst. Neurosci. 4, 22 (2010)Google Scholar
  9. 9.
    Harriger, L., Heuvel, M.P., Sporns, O.: Rich club organization of macaque cerebral cortex and its role in network communication. PloS One 7(9), e46497 (2012)CrossRefGoogle Scholar
  10. 10.
    Hayasaka, S., Laurienti, P.J.: Comparison of characteristics between region-and voxel-based network analyses in resting-state fMRI data. NeuroImage 50(2), 499–508 (2010)CrossRefGoogle Scholar
  11. 11.
    Heuvel, M.P., Stam, C.J., Boersma, M., Hulshoff Pol, H.E.: Small-world and scale-free organization of voxel-based resting-state functional connectivity in the human brain. NeuroImage 43(3), 528–539 (2008)CrossRefGoogle Scholar
  12. 12.
    Heuvel, M.P., Sporns, O.: Rich-club organization of the human connectome. J. Neurosci. 31(44), 15775–15786 (2011)CrossRefGoogle Scholar
  13. 13.
    Essen, D.C., Smith, S.M., Barch, D.M., Behrens, T.E.J., Yacoub, E., Ugurbil, K.: The WU-Minn human connectome project: an overview. NeuroImage 80, 62–79 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Riccardo Zucca
    • 1
    Email author
  • Xerxes D. Arsiwalla
    • 1
  • Hoang Le
    • 2
  • Mikail Rubinov
    • 3
    • 4
  • Paul F. M. J. Verschure
    • 1
    • 5
  1. 1.Laboratory of Synthetic Perceptive, Emotive and Cognitive Systems (SPECS), N-RAS, DTICUniversitat Pompeu Fabra (UPF)BarcelonaSpain
  2. 2.California Institute of TechnologyPasadenaUSA
  3. 3.Department of Psychiatry, Behavioural and Clinical Neuroscience InstituteUniversity of CambridgeCambridgeUK
  4. 4.Janelia Research CampusHoward Hughes Medical InstituteAshburnUSA
  5. 5.Catalan Institute of Advanced Studies (ICREA)BarcelonaSpain

Personalised recommendations