How Close to Optimal Are Small World Properties of Human Brain Networks?

  • Conference paper
  • First Online:
Models, Algorithms, and Technologies for Network Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 32))

  • 1138 Accesses

Abstract

A number of studies have reported small-world properties in human brain networks. Recently Barmpoutis et al. [2] have shown that there exist networks with optimal small-world structure, in the sense that they optimize all small-world attributes compared to other networks of given order and size. We wished to evaluate how close human brain network properties are compared to the properties of optimal small-world networks. We have constructed weighted functional human brain networks based on functional magnetic resonance imaging (fMRI) data and MNI anatomical parcellation of brain. These weighted networks were further thresholded in order to obtain a set of simple undirected graphs. In the obtained graphs we computed small-world characteristics and compared them to the characteristics of comparable optimal small-world networks.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (Canada)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  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. 26(1), 63 (2006)

    Article  Google Scholar 

  2. Barmpoutis, D., Murray, R.: Networks with the smallest average distance and the largest average clustering. Arxiv preprint ar**v:1007.4031 (2010) http://arxiv.org/abs/1007.4031

  3. Barmpoutis, D., Murray, R.: Extremal properties of complex networks. Arxiv preprint ar**v:1104.5532 (2011) http://arxiv.org/abs/1104.5532

  4. Eguiluz, V., Chialvo, D., Cecchi, G., Baliki, M., Apkarian, A.: Scale-free brain functional networks. Phys. Rev. Lett. 94(1), 18, 102 (2005)

    Google Scholar 

  5. Hilgetag, C., Burns, G., O’Neill, M., Scannell, J., Young, M.: Anatomical connectivity defines the organization of clusters of cortical areas in the macaque and the cat. Philosophical Transactions of the Royal Society of London. Series B: Biol. Sci. 355(1393), 91–110 (2000)

    Article  Google Scholar 

  6. Hong, H., Choi, M., Kim, B.: Synchronization on small-world networks. Phys. Rev. E 65(2), 026,139 (2002)

    Google Scholar 

  7. Latora, V., Marchiori, M.: Economic small-world behavior in weighted networks. The Eur. Phys. J. B 32(2), 249–263 (2003)

    Article  Google Scholar 

  8. Laughlin, S., Sejnowski, T.: Communication in neuronal networks. Science 301(5641), 1870 (2003)

    Article  Google Scholar 

  9. Percival, D., Walden, A.: Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge (2006)

    MATH  Google Scholar 

  10. Pinker, S.: The Better Angels of Our Nature: Why Violence Has Declined. Viking Adult, New York (2011)

    Google Scholar 

  11. Salvador, R., Suckling, J., Coleman, M., Pickard, J., Menon, D., Bullmore, E.: Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb. Cortex 15(9), 1332–1342 (2005)

    Article  Google Scholar 

  12. Skidmore, F., Korenkevych, D., Liu, Y., He, G., Bullmore, E., Pardalos, P.: Connectivity brain networks based on wavelet correlation analysis in parkinson fmri data. Neurosci. Lett. 499(1), 47–51 (2011)

    Article  Google Scholar 

  13. Stam, C.: Functional connectivity patterns of human magnetoencephalographic recordings: a ‘small-world’ network? Neurosci. Lett. 355(1–2), 25–28 (2004)

    Article  Google Scholar 

  14. Stephan, K., Hilgetag, C., Burns, G., O’Neill, M., Young, M., Kotter, R.: Computational analysis of functional connectivity between areas of primate cerebral cortex. Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 355(1393), 111 (2000)

    Article  Google Scholar 

  15. Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., Joliot, M.: Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15(1), 273–289 (2002)

    Article  Google Scholar 

  16. Watts, D., Strogatz, S.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dmytro Korenkevych .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this paper

Cite this paper

Korenkevych, D., Skidmore, F., Goldengorin, B., Pardalos, P.M. (2013). How Close to Optimal Are Small World Properties of Human Brain Networks?. In: Goldengorin, B., Kalyagin, V., Pardalos, P. (eds) Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5574-5_7

Download citation

Publish with us

Policies and ethics

Navigation