Skip to content

Advertisement

  • Poster presentation
  • Open Access

Hierarchical organization of multiscale communities in brain networks is non-tree structured

BMC Neuroscience201516 (Suppl 1) :P187

https://doi.org/10.1186/1471-2202-16-S1-P187

  • Published:

Keywords

  • Community Structure
  • Functional Module
  • Brain Network
  • Community Detection
  • Hierarchical Organization

In literature of network science, a group of nodes that are densely connected within the group and are less connected with nodes outside the group is referred to as a "community" [1]. Community structure is a fundamental property of a variety of social, biological and engineering networks. Specifically, communities in brain networks are considered to be associated with functional modules of information processing in the brain [2]. To reveal information processing architecture of the brain, therefore, it is pivotal to know individual communities and their organization in brain networks.

Community structure in brain networks is characterized by hierarchical organization, which reflects that functional modules at larger scales are built up from a set of functional modules at smaller scales [3]. A number of mathematical methods for detecting communities in networks have been developed so far [1], but unfortunately few of them can consistently deal with hierarchical organization of multiscale communities. Here we propose a reliable method for detecting hierarchical organization of multiscale communities. Then we examine community structure of real brain networks by use of this method.

The proposed method is based on a novel Bayesian formulation of Markov chain. The method has only one parameter, , which comes from the precision of the prior distribution of a random process. The amplitude of controls the resolution of community detection; the smaller its amplitude, the finer the size of detected communities. Quasi-static increase in causes a series of discrete phase transitions; at each transition point a subset of smaller communities (children) agglomerate a larger community (parent), thus leading to a hierarchical organization of multiscale communities.

Applying this method to the neuronal network of C. elegans [4] and the macaque cortical network [5], we have found that hierarchical organization of multiscale communities in these networks is non-tree structured: Some child communities have more than one parent community (Figure 1). These findings suggest efficient architecture for integration of functional modules in brain information processing: The same functional modules at lower levels can be shared by distinct functional modules at higher levels.
Figure 1
Figure 1

Hierarchical organization of communities in the neuronal network of C. elegans. Each layer of the hierarchy is shown by horizontal alignment of red squares. Each square indicates a community detected at each layer. The size of each square indicates the size of the corresponding community. Note that many communities have more than one link from the upper layer, which means that these communities have more than one parent. These demonstrate non-tree structure of hierarchical organization of communities in the brain network.

Declarations

Acknowledgements

This work was partly supported by JSPS KAKENHI Grant Number 23500379.

Authors’ Affiliations

(1)
RIKEN Brain Science Institute, Saitama 351-0198, Japan
(2)
Research & Development Group, Fuji Xerox Co. Ltd., Kanagawa 220-8668, Japan

References

  1. Newman MEJ: Communities, modules and large-scale structure in networks. Nature Phys. 2012, 8: 25-31.View ArticleGoogle Scholar
  2. Bullmore E, Sporns O: Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Rev Neurosci. 2009, 10 (3): 186-198.View ArticleGoogle Scholar
  3. Meunier D, Lambiotte R, Bullmore ET : Modular and hierarchically modular organization of brain networks. Front Neurosci. 2010, 4: 1-11.View ArticleGoogle Scholar
  4. Watts DJ, Strogatz SH: Collective dynamics of "small-world" networks. Nature. 1998, 393: 440-442.PubMedView ArticleGoogle Scholar
  5. CoCoMac. [http://cocomac.g-node.org/drupal/]

Copyright

© Okamoto 2015

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Advertisement