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The diverse club

M. A. Bertolero, B. T. T. Yeo, M. D’Esposito

Nature Communications · 2017 · CC BY

doi:10.1038/s41467-017-01189-w (opens in a new tab)

Abstract

A complex system can be represented and analyzed as a network, where nodes represent the units of the network and edges represent connections between those units. For example, a brain network represents neurons as nodes and axons between neurons as edges. In many networks, some nodes have a disproportionately high number of edges as well as many edges between each other and are referred to as the “rich club”. In many different networks, the nodes of this club are assumed to support global network integration. Here we show that another set of nodes, which have edges diversely distributed across the network, form a “diverse club”. The diverse club exhibits, to a greater extent than the rich club, properties consistent with an integrative network function—these nodes are more highly interconnected and their edges are more critical for efficient global integration. Finally, these two clubs potentially evolved via distinct selection pressures.

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References 68

  1. 1.

    Bertolero MA, Yeo BTT, D’Esposito M. The modular and integrative functional architecture of the human brain. Proc. Natl Acad. Sci. USA. 2015;112:E6798-E6807.

    Not in our library10.1073/pnas.1510619112 (opens in a new tab)

  2. 2.

    Newman MEJ. Modularity and community structure in networks. Proc. Natl Acad. Sci. USA. 2006;103:8577-8582.

    Not in our library10.1073/pnas.0601602103 (opens in a new tab)

  3. 3.

    Power JD, et al. Functional network organization of the human brain. Neuron. 2011;72:665-678.

    Not in our library10.1016/j.neuron.2011.09.006 (opens in a new tab)

  4. 4.

    Yeo BTT, et al. The organization of the human cerebral cortex estimated by intrinsic functional connectivity. J. Neurophysiol. 2011;106:1125-1165.

    Not in our library10.1152/jn.00338.2011 (opens in a new tab)

  5. 5.

    van den Heuvel MP, Sporns O. Rich-club organization of the human connectome. J. Neurosci. 2011;31:15775-15786.

    Not in our library10.1523/jneurosci.3539-11.2011 (opens in a new tab)

  6. 6.

    Power JD, Schlaggar BL, Lessov-Schlaggar CN, Petersen SE. Evidence for Hubs in human functional brain. Networks. 2013;79:798-813.

    Not in our library10.1016/j.neuron.2013.07.035 (opens in a new tab)

  7. 7.

    Schmidt R, LaFleur KJR, de Reus MA, van den Berg LH, van den Heuvel MP. Kuramoto model simulation of neural hubs and dynamic synchrony in the human cerebral connectome. BMC Neurosci. 2015;16:143.

    Not in our library10.1186/1471-2202-16-s1-p143 (opens in a new tab)

  8. 8.

    Liska A, Galbusera A, Schwarz AJ, Gozzi A. Functional connectivity hubs of the mouse brain. Neuroimage. 2015;115:281-291.

    Not in our library10.1016/j.neuroimage.2015.04.033 (opens in a new tab)

  9. 9.

    Scholtens LH, Schmidt R, de Reus MA, van den Heuvel MP. Linking macroscale graph analytical organization to microscale neuroarchitectonics in the macaque connectome. J. Neurosci. 2014;34:12192-12205.

    Not in our library10.1523/jneurosci.0752-14.2014 (opens in a new tab)

  10. 10.

    Guimerà R, Guimera R, Amaral LAN, Amaral L. Functional cartography of complex metabolic networks. Nature. 2005;433:895-900.

    Not in our library10.1038/nature03288 (opens in a new tab)

  11. 11.

    Guimera R, Mossa S, Turtschi A, Amaral LAN. The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proc. Natl Acad. Sci. USA. 2005;102:7794-7799.

    Not in our library10.1073/pnas.0407994102 (opens in a new tab)

  12. 12.

    Guimerà R, Sales-Pardo M, Amaral LAN. Classes of complex networks defined by role-to-role connectivity profiles. Nat. Phys. 2007;3:63-69.

    Not in our library10.1038/nphys489 (opens in a new tab)

  13. 13.

    Towlson EK, Vértes PE, Ahnert SE, Schafer WR, Bullmore ET. The Rich Club of the C. elegans neuronal connectome. J. Neurosci. 2013;33:6380-6387.

    Not in our library10.1523/jneurosci.3784-12.2013 (opens in a new tab)

  14. 14.
  15. 15.
  16. 16.
  17. 17.
  18. 18.

    van den Heuvel MP, Sporns O. An anatomical substrate for integration among functional networks in human cortex. J. Neurosci. 2013;33:14489-14500.

    Not in our library10.1523/jneurosci.2128-13.2013 (opens in a new tab)

  19. 19.

    Alstott J, Panzarasa P, Rubinov M, Bullmore ET, Vértes PE. A unifying framework for measuring weighted rich clubs. Sci. Rep. 2014;4:7258.

    Not in our library10.1038/srep07258 (opens in a new tab)

  20. 20.

    Colizza V, Flammini A, Serrano MA, Vespignani A. Detecting rich-club ordering in complex networks. Nat. Phys. 2006;2:110-115.

    Not in our library10.1038/nphys209 (opens in a new tab)

  21. 21.

    de Reus MA, van den Heuvel MP. Rich club organization and intermodule communication in the cat connectome. J. Neurosci. 2013;33:12929-12939.

    Not in our library10.1523/jneurosci.1448-13.2013 (opens in a new tab)

  22. 22.

    Bullmore E, Sporns O. The economy of brain network organization. Nat. Rev. Neurosci. 2012;74:47-14.

    Not in our library10.1038/nrn3214 (opens in a new tab)

  23. 23.

    Bassett DS, Yang M, Wymbs NF, Grafton ST. Learning-induced autonomy of sensorimotor systems. Nat. Neurosci. 2015;18:744-751.

    Not in our library10.1038/nn.3993 (opens in a new tab)

  24. 24.

    Spadone S, et al. Dynamic reorganization of human resting-state networks during visuospatial attention. Proc. Natl Acad. Sci. USA. 2015;112:8112-8117.

    Not in our library10.1073/pnas.1415439112 (opens in a new tab)

  25. 25.
  26. 26.

    Cole MW, et al. Multi-task connectivity reveals flexible hubs for adaptive task control. Nat. Neurosci. 2013;16:1348-1355.

    Not in our library10.1038/nn.3470 (opens in a new tab)

  27. 27.

    Yeo BTT, et al. Functional specialization and flexibility in human association cortex. Cereb. Cortex. 2015;26:465-465.

    Not in our library10.1093/cercor/bhv260 (opens in a new tab)

  28. 28.

    Gratton C, Nomura EM, Pérez F, D’Esposito M. Focal brain lesions to critical locations cause widespread disruption of the modular organization of the brain. J. Cogn. Neurosci. 2012;24:1275-1285.

    Not in our library10.1162/jocn_a_00222 (opens in a new tab)

  29. 29.

    Warren DE, et al. Network measures predict neuropsychological outcome after brain injury. Proc. Natl Acad. Sci. USA. 2014;111:14247-14252.

    Not in our library10.1073/pnas.1322173111 (opens in a new tab)

  30. 30.
  31. 31.

    Cajal, S. R. Y. Texture of the Nervous System of Man and the Vertebrates (Springer Vienna, 2000). doi:10.1007/978-3-7091-6315-3

    Not in our library

  32. 32.

    Bassett DS, Bullmore E. Small-world brain networks. Neuroscientist. 2006;12:512-523.

    Not in our library10.1177/1073858406293182 (opens in a new tab)

  33. 33.

    Fornito A, et al. Genetic influences on cost-efficient organization of human cortical functional networks. J. Neurosci. 2011;31:3261-3270.

    Not in our library10.1523/jneurosci.4858-10.2011 (opens in a new tab)

  34. 34.

    Bassett DS, et al. Cognitive fitness of cost-efficient brain functional networks. Proc. Natl Acad. Sci. USA. 2009;106:11747-11752.

    Not in our library10.1073/pnas.0903641106 (opens in a new tab)

  35. 35.

    Langer N, et al. Functional brain network efficiency predicts intelligence. Hum. Brain Mapp. 2011;33:1393-1406.

    Not in our library10.1002/hbm.21297 (opens in a new tab)

  36. 36.

    Khundrakpam BS, et al. Imaging structural covariance in the development of intelligence. Neuroimage. 2017;144:227-240.

    Not in our library10.1016/j.neuroimage.2016.08.041 (opens in a new tab)

  37. 37.
  38. 38.

    Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature. 1998;393:440-442.

    Not in our library10.1038/30918 (opens in a new tab)

  39. 39.

    Deco G, et al. Rethinking segregation and integration: contributions of whole-brain modelling. Nat. Rev. Neurosci. 2015;16:430-439.

    Not in our library10.1038/nrn3963 (opens in a new tab)

  40. 40.

    Zamora-López G, Chen Y, Deco G, Kringelbach ML, Zhou C. Functional complexity emerging from anatomical constraints in the brain: the significance of network modularity and rich-clubs. Sci Rep. 2016;6:38424.

    Not in our library10.1038/srep38424 (opens in a new tab)

  41. 41.

    Simon, H. A. in Facets of Systems Science 457–476 (Springer, 1991). doi:10.1007/978-1-4899-0718-9_31

    Not in our library

  42. 42.

    Fodor, J. & Fodor, J. The Modularity of Mind (MIT Press, 1983).

    Not in our library

  43. 43.

    Coltheart M. Modularity and cognition. Trends Cogn. Sci. 1999;3:115-120.

    Not in our library10.1016/s1364-6613(99)01289-9 (opens in a new tab)

  44. 44.

    Robinson PA, Henderson JA, Matar E, Riley P, Gray RT. Dynamical reconnection and stability constraints on cortical network architecture. Phys. Rev. Lett. 2009;103:108104.

    Not in our library10.1103/physrevlett.103.108104 (opens in a new tab)

  45. 45.
  46. 46.

    Tosh CR, Tosh CR, McNally L, McNally L. The relative efficiency of modular and non-modular networks of different size. Proc. Biol. Sci. 2015;282:20142568-20142568.

    Not in our library10.1098/rspb.2014.2568 (opens in a new tab)

  47. 47.
  48. 48.

    Arnemann KL, et al. Functional brain network modularity predicts response to cognitive training after brain injury. Neurology. 2015;84:1568-1574.

    Not in our library10.1212/wnl.0000000000001476 (opens in a new tab)

  49. 49.
  50. 50.

    Gollo LL, Zalesky A, Hutchison RM, van den Heuvel M, Breakspear M. Dwelling quietly in the rich club: brain network determinants of slow cortical fluctuations. Philos. Trans. R. Soc. Lond. B Biol. Sci. 2015;370:20140165-20140165.

    Not in our library10.1098/rstb.2014.0165 (opens in a new tab)

  51. 51.

    Margulies DS, et al. Situating the default-mode network along a principal gradient of macroscale cortical organization. Proc. Natl Acad. Sci. USA. 2016;113:12574-12579.

    Not in our library10.1073/pnas.1608282113 (opens in a new tab)

  52. 52.

    Nguyen JP, et al. Whole-brain calcium imaging with cellular resolution in freely behaving Caenorhabditis elegans. Proc. Natl Acad. Sci. USA. 2016;113:E1074-E1081.

    Not in our library10.1073/pnas.1507110112 (opens in a new tab)

  53. 53.

    White JG, Southgate E, Thomson JN, Brenner S. The structure of the nervous system of the nematode Caenorhabditis elegans. Phil. Trans. R. Soc. B. 1986;314:1-340.

    Not in our library10.1098/rstb.1986.0056 (opens in a new tab)

  54. 54.

    Van Essen DC, et al. The WU-Minn human connectome project: an overview. Neuroimage. 2013;80:62-79.

    Not in our library10.1016/j.neuroimage.2013.05.041 (opens in a new tab)

  55. 55.

    Cox RW. AFNI: software for analysis and visualization of functional magnetic resonance neuroimages. Comput. Biomed. Res. 1996;29:162-173.

    Not in our library10.1006/cbmr.1996.0014 (opens in a new tab)

  56. 56.

    Young MP. The organization of neural systems in the primate cerebral cortex. Proc. R. Soc. B Biol. Sci. 1993;252:13-18.

    Not in our library10.1098/rspb.1993.0040 (opens in a new tab)

  57. 57.

    Newman MEJ, Girvan M. Finding and evaluating community structure in networks. Phys. Rev. E. 2004;69:026113.

    Not in our library10.1103/physreve.69.026113 (opens in a new tab)

  58. 58.

    Reichardt J, Bornholdt S. Statistical mechanics of community detection. Phys. Rev. E. 2006;74:016110.

    Not in our library10.1103/physreve.74.016110 (opens in a new tab)

  59. 59.

    Newman MEJ. Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E. 2006;74:036104.

    Not in our library10.1103/physreve.74.036104 (opens in a new tab)

  60. 60.

    Blondel VD, Guillaume J-L, Lambiotte R, Lefebvre E. Fast unfolding of communities in large networks. J. Stat. Mech. Theory Exp. 2008;2008:P10008.

    Not in our library10.1088/1742-5468/2008/10/p10008 (opens in a new tab)

  61. 61.

    Raghavan UN, Albert R, Kumara S. Near linear time algorithm to detect community structures in large-scale networks. Phys. Rev. E. 2007;76:036106.

    Not in our library10.1103/physreve.76.036106 (opens in a new tab)

  62. 62.

    Girvan M, Newman MEJ. Community structure in social and biological networks. Proc. Natl Acad. Sci. USA. 2002;99:7821-7826.

    Not in our library10.1073/pnas.122653799 (opens in a new tab)

  63. 63.
  64. 64.

    Pons P, Latapy M. Computing communities in large networks using random walks. J. Graph Algorithms Appl. 2006;11:259-276.

    Not in our library

  65. 65.

    Rosvall M, Rosvall M, Bergstrom CT, Bergstrom CT. Maps of random walks on complex networks reveal community structure. Proc. Natl Acad. Sci. USA. 2008;105:1118-1123.

    Not in our library10.1073/pnas.0706851105 (opens in a new tab)

  66. 66.

    Fortunato S, Barthélemy M. Resolution limit in community detection. Proc. Natl Acad. Sci. USA. 2007;104:36-41.

    Not in our library10.1073/pnas.0605965104 (opens in a new tab)

  67. 67.
  68. 68.

    Delvenne JC, Yaliraki SN, Barahona M. Stability of graph communities across time scales. Proc. Natl Acad. Sci. USA. 2010;107:12755-12760.

    Not in our library10.1073/pnas.0903215107 (opens in a new tab)

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