Cited by 1,156Functional Brain Connectivity StudiesComplex Network Analysis TechniquesAdvanced Neuroimaging Techniques and Applications

Modular and hierarchically modular organization of brain networks

Open access
Meunier, David, Lambiotte, Renaud, Bullmore, Edward T.·2010·Frontiers in Neuroscience

Abstract

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.3389/fnins.2010.00200

Cites

6 of 6 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Free energy may be most effectively minimized-and integrated information maximized-if synchronized couplings take the form of hierarchically organized modules, thus affording robustness, separable optimization, balanced integration and differentiation, evolvability via degeneracy, efficient communication via small-world connectivity, and flexible multi-scale responsivity via critical dynamics.

    “Free energy may be most effectively minimized—and integrated information maximized (Marshall et al., 2016)—if synchronized couplings take the form of hierarchically organized modules, thus affording robustness, separable optimization, balanced integration and differentiation, evolvability via degeneracy, efficient communication via small-world connectivity, and flexible multi-scale responsivity”

    From An Integrated World Modeling Theory (IWMT) of Consciousness (2020) · cites this paper as Meunier et al., 2010

    Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 71

  1. Achard S. Salvador R. Whitcher B. Suckling J. Bullmore E. (2006). A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J. Neurosci. 26, 63– 72 10.1523/JNEUROSCI.3874-05.2006 16399673 PMC6674299 · DOI · Paper page
  2. Ahn Y-Y. Bagrow J. P. Lehmann S. (2010). Link communities reveal multiscale complexity in networks. Nature 466, 761– 764 10.1038/nature09182 20562860 · DOI
  3. Alexander-Bloch A. F. Gogtay N. Meunier D. Birn R. Clasen L. Lalonde F. Lenroot R. Giedd J. Bullmore E. T. (2010). Disrupted modularity and local connectivity of brain functional networks in childhood-onset schizophrenia. Front. Syst. Neurosci. 4: 147 10.3389/fnsys.2010.00147 21031030 PMC2965020 · DOI · Paper page
  4. Barthélemy M. (2010). Spatial networks. ARXIV 2010arXiv1010.0302B.
  5. Bassett D. S. Bullmore E. T. (2006). Small-world brain networks. Neuroscientist 12, 512– 523 10.1177/1073858406293182 17079517 · DOI · Paper page
  6. Bassett D. S. Bullmore E. Verchinski B. A. Mattay V. S. Weinberger D. R. Meyer-Lindenberg A. (2008). Hierarchical organization of human cortical networks in health and schizophrenia. J. Neurosci. 28, 9239– 9248 10.1523/JNEUROSCI.1929-08.2008 18784304 PMC2878961 · DOI
  7. Bassett D. S. Greenfield D. L. Meyer-Lindenberg A. Weinberger D. R. Moore S. W. Bullmore E. (2010). Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput. Biol. 6, 1000748 10.1371/journal.pcbi.1000748 PMC2858671 20421990 · DOI
  8. Bullmore E. Barnes A. Bassett D. S. Fornito A. Kitzbichler M. Meunier D. Suckling J. (2009). Generic aspects of complexity in brain imaging data and other biological systems. NeuroImage 47, 1125– 1134 10.1016/j.neuroimage.2009.05.032 19460447 · DOI
  9. Bullmore E. Bassett D. S. (2010). Brain graphs: graphical models of the human brain connectome. Ann. Rev. Clin. Psychol. 10.1146/annurev-clinpsy-040510-143934 21128784 · DOI
  10. Bullmore E. Sporns O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186– 198 10.1038/nrn2575 19190637 · DOI · Paper page
  11. Buzsáki G. Draguhn A. (2004). Neuronal oscillations in cortical networks. Science 304, 1926– 1929 10.1126/science.1099745 15218136 · DOI · Paper page
  12. Calhoun V. D. Kiehl K. A. Pearlson G. D. (2008). Modulation of temporally coherent brain networks estimated using ICA at rest and during cognitive tasks. Hum. Brain Mapp. 29, 828– 838 10.1002/hbm.20581 18438867 PMC2649823 · DOI · Paper page
  13. Chavez M. Valencia M. Navarro V. Latora V. Martinerie J. (2010). Functional modularity of background activities in normal and epileptic brain networks. Phys. Rev. Lett. 104, 118701 10.1103/PhysRevLett.104.118701 20366507 · DOI
  14. Chen Z. J. He Y. Rosa-Neto P. Germann J. Evans A. C. (2008). Revealing modular architecture of human brain structural networks by using cortical thickness from MRI. Cereb. Cortex 18, 2374– 2381 10.1093/cercor/bhn003 18267952 PMC2733312 · DOI · Paper page
  15. Clauset A. Moore C. Newman M. E. J. (2008). Hierarchical structure and the prediction of missing links in networks. Nature 453, 98– 101 10.1038/nature06830 18451861 · DOI · Paper page
  16. Dehaene S. Kerszberg M. Changeux J.-P. (1998). A neuronal model of a global workspace in effortful cognitive tasks. Proc. Natl. Acad. Sci. U.S.A. 95, 14529– 14534 10.1073/pnas.95.24.14529 9826734 PMC24407 · DOI · Paper page
  17. Delvenne J.-C. Yaliraki S. Barahona M. (2010). Stability of graph communities across time scales. Proc. Natl. Acad. Sci. U.S.A. 107, 12755– 12760 10.1073/pnas.0903215107 20615936 PMC2919907 · DOI
  18. Evans T. S. Lambiotte R. (2009). Line graphs, link partitions and overlapping communities. Phys. Rev. E. 80, 016105 10.1103/PhysRevE.80.016105 19658772 · DOI
  19. Ferrarini L. Veer I. M. Baerends E. van Tol M.-J. Renken R. J. van der Wee N. J. Veltman D. J. Aleman A. Zitman F. G. Penninx B. W. van Buchem M. A. Reiber J. H. Rombouts S. A. Milles J. (2009). Hierarchical functional modularity in the resting-state human brain. Hum. Brain Mapp. 30, 2220– 2231 10.1002/hbm.20663 18830955 PMC6871119 · DOI
  20. Fodor J. A. (1983). The Modularity of Mind: An Essay on Faculty Psychology. Cambridge, MA: MIT Press
  21. Fortunato S. (2010). Community detection in graphs. Phys. Rep. 486, 75– 174 10.1016/j.physrep.2009.11.002 · DOI · Paper page
  22. Freeman L. (1979). Centrality in networks: I. Conceptual clarification. Soc. Networks 1, 215– 239 10.1016/0378-8733(78)90021-7 · DOI · Paper page
  23. Gross T. Blasius B. (2008). Adaptive coevolutionary networks: a review. J. R. Soc. Interface 5, 259– 271 10.1098/rsif.2007.1229 17971320 PMC2405905 · DOI
  24. Guimerà R. Sales-Pardo M. Amaral L. A. (2004). Modularity from fluctuations in random graphs and complex networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 025101 10.1103/PhysRevE.70.025101 15447530 PMC2441765 · DOI · Paper page
  25. He Y. Chen Z. J. Evans A. C. (2007). Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. Cereb. Cortex 10, 149– 162 17204824
  26. He Y. Evans A. C. (2010). Graph theoretical modeling of brain connectivity. Curr. Opin. Neurol. 23, 341– 350 20581686
  27. He Y. Wang J. Wang L. Chen Z. J. Yan C. Yang H. Tang H. Zhu C. Gong Q. Zang Y. Evans A. C. (2009). Uncovering intrinsic modular organization of spontaneous brain activity in humans. PLoS One 4, e5226 10.1371/journal.pone.0005226 19381298 PMC2668183 · DOI
  28. Hilgetag C.-C. Burns G. A. P. C. O'Neill M. A. Scannell J. W. (2000). Anatomical connectivity defines the organization of clusters of cortical areas in the macaque and the cat. Philos. Trans. R. Soc. Lond. B. Biol. Sci. 355, 91– 110 10.1098/rstb.2000.0551 10703046 PMC1692723 · DOI
  29. Hütt M.-T. Lesne A. (2009). Interplay between topology and dynamics in excitation patterns on hierarchical graphs. Front. Neuroinformatics 3: 28 10.3389/neuro.11.028.2009 19826610 PMC2759346 · DOI
  30. Jarvis S. Rotter S. Egert U. (2010). Extending stability through hierarchical clusters in echo state networks. Front. Neuroinformatics 4: 1 10.3389/fninf.2010.00011 20725523 PMC2914532 · DOI
  31. Kaiser M. Gorner M. Hilgetag C. C. (2007). Criticality of spreading dynamics in hierarchical cluster networks without inhibition. New J. Phys. 9, 110 10.1088/1367-2630/9/5/110 · DOI
  32. Kaiser M. Hilgetag C. C. (2006). Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. 2, e95 10.1371/journal.pcbi.0020095 16848638 PMC1513269 · DOI
  33. Kaiser M. Hilgetag C. C. (2010). Optimal hierarchical modular topologies for producing limited sustained activation of neural networks. Front. Neuroinformatics 4: 8 10.3389/fninf.2010.00008 20514144 PMC2876872 · DOI
  34. Kashtan N. Alon U. (2005). Spontaneous evolution of modularity and network motifs. Proc. Natl. Acad. Sci. U.S.A. 102, 13773– 13778 10.1073/pnas.0503610102 16174729 PMC1236541 · DOI
  35. Lambiotte R. (2010). “Multi-scale modularity in complex networks” in 2010 Proceedings of the 8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), 546– 553
  36. Latora V. Marchiori M. (2001). Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 10.1103/PhysRevLett.87.198701 11690461 · DOI · Paper page
  37. Meunier D. Lambiotte R. Fornito A. Ersche K. Bullmore E. T. (2009a). Hierarchical modularity in human brain functional networks. Front. Neuroinformatics 3: 37 10.3389/neuro.11.037.2009 19949480 PMC2784301 · DOI
  38. Meunier D. Achard S. Morcom A. Bullmore E. (2009b). Age-related changes in modular organization of human brain functional networks. NeuroImage 44, 715– 723 10.1016/j.neuroimage.2008.09.062 19027073 · DOI · Paper page
  39. Müller-Linow M. Hilgetag C. C. Hütt M. T. (2008). Organization of excitable dynamics in hierarchical biological networks. PLoS Comput. Biol. 4, e100019 10.1371/journal.pcbi.1000190 PMC2542420 18818769 · DOI
  40. Newman M. (2003). The structure and function of complex networks. SIAM Rev. 45, 167– 256 10.1137/S003614450342480 · DOI · Paper page
  41. Palla G. Derenyi I. Farkas I. Vicsek T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814– 818 10.1038/nature03607 15944704 · DOI · Paper page
  42. Pan R. K. Chatterjee N. Sinha S. (2010). Mesoscopic organization reveals the constraints governing Caenorhabditis elegans nervous system. PLoS One 5, e9240 10.1371/journal.pone.0009240 20179757 PMC2825259 · DOI
  43. Pan R. K. Sinha S. (2009). Modularity produces small-world networks with dynamical time-scale separation. Europhys. Lett. 85, 68006 10.1209/0295-5075/85/68006 · DOI
  44. Reichardt J. Bornholdt S. (2004). Detecting fuzzy community structures in complex networks with a Potts model. Phys. Rev. Lett. 93, 218701 10.1103/PhysRevLett.93.218701 15601068 · DOI
  45. Redies C. Puelles L. (2001). Modularity in vertebrate brain development and evolution. Bioessays 23, 1100– 1111 10.1002/bies.10014 11746229 · DOI
  46. Reijneveld J. C. Ponten S. C. Berendse H. W. Stam C. J. (2007). The application of graph theoretical analysis to complex networks in the brain. Clin. Neurophys. 118, 2317– 2331 10.1016/j.clinph.2007.08.010 17900977 · DOI
  47. Robinson P. A. Henderson J. A. Matar E. Riley P. Gray R. T. (2009). Dynamical reconnection and stability constraints on cortical network architecture. Phys. Rev. Lett. 103, 108104 10.1103/PhysRevLett.103.108104 19792345 · DOI
  48. Rosvall M. Bergstrom C. T. (2008). Maps of random walks on complex networks reveal community structure. Proc. Natl. Acad. Sci. U.S.A. 105, 1118– 1123 10.1073/pnas.0706851105 18216267 PMC2234100 · DOI · Paper page
  49. Rubinov M. Sporns O. (2010). Complex network measures of brain connectivity: uses and interpretations. NeuroImage 52, 1059– 1069 10.1016/j.neuroimage.2009.10.003 19819337 · DOI · Paper page
  50. Rubinov M. Sporns O. van Leeuwen C. Breakspear M. (2009). Symbiotic relationship between brain structure and dynamics. BMC Neurosci. 10, 55 10.1186/1471-2202-10-55 19486538 PMC2700812 · DOI
  51. Sales-Pardo M. Guimerà R. Moreira A. A. Amaral L. A. N. (2007). Extracting the hierarchical organization of complex systems. Proc. Natl. Acad. Sci. U.S.A. 104, 15224– 15229 10.1073/pnas.0703740104 17881571 PMC2000510 · DOI
  52. Salvador R. Suckling J. Coleman M. Pickard J. Menon D. Bullmore E. (2005). Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb. Cortex 15, 1332– 1342 10.1093/cercor/bhi016 15635061 · DOI
  53. Schwarz A. J. Gozzi A. Bifone A. (2009). Community structure in networks of functional connectivity: resolving functional organization in the rat brain with pharmacological MRI. Neuroimage 47, 302– 311 10.1016/j.neuroimage.2009.03.064 19345737 · DOI
  54. Shanahan M. (2008). Dynamical complexity in small-world networks of spiking neurons. Phys. Rev. E. 78, 041924 10.1103/PhysRevE.78.041924 18999472 · DOI
  55. Shanahan M. (2010). Metastable chimera states in community-structured oscillator networks. Chaos 20, 013108 10.1063/1.3305451 20370263 · DOI
  56. Simon H. A. (1962). The architecture of complexity. Proc. Am. Philos. Soc. 106, 467– 482
  57. Simon H. A. (1995). “Near-decomposability and complexity: How a mind resides in a brain,” in The Mind, the Brain, and Complex Adaptive Systems, eds Morowitz H. Singer J. (Reading, MA: Addison-Wesley), pp. 25– 43
  58. Smith S. M. Fox P. T. Miller K. L. Glahn D. C. Fox P. M. Mackay C. E. Filippini N. Watkins K. E. Toro R. Laird A. R. Beckmann C. F. (2009). Correspondence of the brain's functional architecture during activation and rest. Proc. Natl. Acad. Sci. U.S.A. 106, 13040– 13045 10.1073/pnas.0905267106 19620724 PMC2722273 · DOI · Paper page
  59. Sporns O. (2010). Networks of the Brain. Cambridge MA: MIT Press
  60. Sporns O. Chialvo D. Kaiser M. Hilgetag C. C. (2004). Organization, development and function of complex rain networks. Trends Cogn. Sci. 8, 418– 425 10.1016/j.tics.2004.07.008 15350243 · DOI · Paper page
  61. Sporns O. Honey C. Kötter R. (2007). Identification and classification of hubs in brain networks. PLoS One 2, e1049 10.1371/journal.pone.0001049 17940613 PMC2013941 · DOI · Paper page
  62. Sporns O. Tononi G. Edelman G. (2000). Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb. Cortex 10, 127– 141 10.1093/cercor/10.2.127 10667981 · DOI
  63. Stam C. J. (2004). Functional connectivity patterns of human magnetoencephalographic recordings: a “small-world” network? Neurosci. Lett. 355, 25– 28 10.1016/j.neulet.2003.10.063 14729226 · DOI
  64. Valencia M. Pastor M. Fernandez-Seara M. Artieda J. Martinerie J. Chavez M. (2009). Complex modular structure of large-scale brain networks. Chaos 19, 23119 10.1063/1.3129783 19566254 · DOI
  65. Van den Heuvel M. Mandl R. Hulshoff Pol H. (2008). Normalized cut group clustering of resting-state fMRI data. PLoS One 3, e2001 10.1371/journal.pone.0002001 18431486 PMC2291558 · DOI
  66. Varela F. Lachaux J. P. Rodriguez E. Martinerie J. (2001). The brainweb: phase synchronization and large-scale integration. Nat Rev. Neurosci. 2, 229– 239 10.1038/35067550 11283746 · DOI · Paper page
  67. Wang J. Zuo X. He Y. (2010). Graph-based network analysis of resting-state functional MRI. Front. Syst. Neurosci. 4: 16 10.3389/fnsys.2010.00016 20589099 PMC2893007 · DOI · Paper page
  68. Watts D. J. Strogatz S. H. (1998). Collective dynamics of “small-world” networks. Nature 393, 440– 442 10.1038/30918 9623998 · DOI · Paper page
  69. Zamora-Lopez G. Zhou C. Kurths J. (2010). Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks. Front. Neuroinformatics 4: 1 10.3389/neuro.11.001.2010 20428515 PMC2859882 · DOI
  70. Zeki S. Bartels A. (1998). The autonomy of the visual systems and the modularity of conscious vision. Phil. Trans. R. Soc. Lond. B., Biol. Sci. 353, 1911– 1914 10.1098/rstb.1998.0343 9854263 PMC1692424 · DOI
  71. Zhou C. Zemanova L. Zamora G. Hilgetag C. C. Kurths J. (2006). Hierarchical oganization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett. 97, 238103 10.1103/PhysRevLett.97.238103 17280251 · DOI

Cited by

Sorted by citations

Authors
Meunier, D., Lambiotte, R., & Bullmore, E. T.
Affiliations
  • Imperial College London (GB)
  • University of Cambridge (GB)
Corresponding author
Bullmore, Edward T.
Venue
Frontiers in Neuroscience
Published
2010
Volume
4
Pages
200-200
ISSN
  • 1662-453X (ISSN-L)
  • 1662-4548
OpenAlex
W2021947606
Cited by
1,156
References
6
Citations by year
2026: 50 · 2025: 75 · 2024: 81 · 2023: 88 · 2022: 79 · 2021: 99 · 2020: 92 · 2019: 78 · 2018: 86 · 2017: 70 · 2016: 86 · 2015: 70 · 2014: 68 · 2013: 65 · 2012: 39
FWCI
25.99
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • Frontiers in Neuroscience (publishedVersion, cc-by)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Repository of the University of Namur (submittedVersion)
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
Keywords
brain networks, hierarchical modularity, modular organization, community structure, structural brain networks, functional brain networks, network topology, network robustness, cortical regions, complex networks

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review