K-shell decomposition reveals hierarchical cortical organization of the human brain

Nir Lahav, Baruch Ksherim, Eti Ben-Simon, Adi Maron-Katz, Reuven Cohen, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


In recent years numerous attempts to understand the human brain were undertaken from a network point of view. A network framework takes into account the relationships between the different parts of the system and enables to examine how global and complex functions might emerge from network topology. Previous work revealed that the human brain features 'small world' characteristics and that cortical hubs tend to interconnect among themselves. However, in order to fully understand the topological structure of hubs, and how their profile reflect the brain's global functional organization, one needs to go beyond the properties of a specific hub and examine the various structural layers that make up the network. To address this topic further, we applied an analysis known in statistical physics and network theory as k-shell decomposition analysis. The analysis was applied on a human cortical network, derived from MRI\DSI data of six participants. Such analysis enables us to portray a detailed account of cortical connectivity focusing on different neighborhoods of inter-connected layers across the cortex. Our findings reveal that the human cortex is highly connected and efficient, and unlike the internet network contains no isolated nodes. The cortical network is comprised of a nucleus alongside shells of increasing connectivity that formed one connected giant component, revealing the human brain's global functional organization. All these components were further categorized into three hierarchies in accordance with their connectivity profile, with each hierarchy reflecting different functional roles. Such a model may explain an efficient flow of information from the lowest hierarchy to the highest one, with each step enabling increased data integration. At the top, the highest hierarchy (the nucleus) serves as a global interconnected collective and demonstrates high correlation with consciousness related regions, suggesting that the nucleus might serve as a platform for consciousness to emerge.

Original languageEnglish
Article number083013
JournalNew Journal of Physics
Issue number8
StatePublished - Aug 2016

Bibliographical note

Funding Information:
Wewould like to thank Mr Kobi Flax for his crucial role in data analysis, without him this work would not be accomplished Wewould also like to thank Dr Itay Hurvitz for his invaluable comments. Wethank the European MULTIPLEX (EU-FET project 317532) project, the Israel Science Foundation, ON Rand DTRA for financial support.

Publisher Copyright:
© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.


  • Consciousness
  • Cortical hubs
  • Graph theory
  • Human brain
  • K-shell decomposition
  • Modular hierarchies in the brain
  • Network theory


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