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  • Review Article
  • Published:

The economy of brain network organization

Key Points

  • Cost control and complex topology are important aspects of the organization of human and other nervous systems.

  • Efficient transfer of information between modules of brain networks confers functional advantages in terms of adaptive behaviour, but it imposes a premium in terms of wiring cost.

  • Brain networks negotiate an economical trade-off between minimizing wiring cost and maximizing expensive but advantageous topological properties such as efficiency.

  • Brain networks can renegotiate trade-offs between cost and efficiency dynamically over short and long timescales.

  • High-cost components of human brain networks may be particularly vulnerable to abnormal development or pathological attack, leading to disorders of cognition or behaviour.

Abstract

The brain is expensive, incurring high material and metabolic costs for its size — relative to the size of the body — and many aspects of brain network organization can be mostly explained by a parsimonious drive to minimize these costs. However, brain networks or connectomes also have high topological efficiency, robustness, modularity and a 'rich club' of connector hubs. Many of these and other advantageous topological properties will probably entail a wiring-cost premium. We propose that brain organization is shaped by an economic trade-off between minimizing costs and allowing the emergence of adaptively valuable topological patterns of anatomical or functional connectivity between multiple neuronal populations. This process of negotiating, and re-negotiating, trade-offs between wiring cost and topological value continues over long (decades) and short (millisecond) timescales as brain networks evolve, grow and adapt to changing cognitive demands. An economical analysis of neuropsychiatric disorders highlights the vulnerability of the more costly elements of brain networks to pathological attack or abnormal development.

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Figure 1: Allometric and fractal scaling of brains and human brain networks.
Figure 2: Hubs and modules in the brain.
Figure 3: Economical trade-offs between wiring cost and topological efficiency of brain networks.
Figure 4: Brain disorders affect high-cost components of networks.

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References

  1. Albert, R. & Barabasi, A. L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002).

    Article  Google Scholar 

  2. Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440–442 (1998).

    Article  CAS  PubMed  Google Scholar 

  3. Bullmore, E. & Sporns, O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Rev. Neurosci. 10, 186–198 (2009).

    Article  CAS  Google Scholar 

  4. Barrat, A., Barthelemy, M. & Vespignani, A. Dynamical Processes on Complex Networks (Cambridge Univ. Press, 2008).

    Book  Google Scholar 

  5. Sporns, O. Networks of the Brain (MIT Press, 2011).

    Google Scholar 

  6. Vidal, M., Cusick, M. E. & Barabasi, A. L. Interactome networks and human disease. Cell 144, 986–998 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Barabasi, A. L. & Oltvai, Z. N. Network biology: understanding the cell's functional organization. Nature Rev. Genet. 5, 101–113 (2004).

    Article  CAS  PubMed  Google Scholar 

  8. Li, S. et al. A map of the interactome network of the metazoan C. elegans. Science 303, 540–543 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Vespignani, A. Modelling dynamical processes in complex socio-technical systems. Nature Phys. 8, 32–39 (2012).

    Article  CAS  Google Scholar 

  10. Barrat, A., Barthelemy, M. & Vespignani, A. The effects of spatial constraints on the evolution of weighted complex networks. J. Stat. Mech. 2005, P05003 (2005).

    Article  Google Scholar 

  11. Sporns, O., Tononi, G. & Edelman, G. M. Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb. Cortex 10, 127–141 (2000).

    Article  CAS  PubMed  Google Scholar 

  12. Bebber, D. P., Hynes, J., Darrah, P. R., Boddy, L. & Fricker, M. D. Biological solutions to transport network design. Proc. R. Soc. B 274, 2307–2315 (2007).

    Article  PubMed  PubMed Central  Google Scholar 

  13. Vertes, P. E. et al. Topological isomorphisms of human brain and financial networks. Front. Syst. Neurosci. 5, 75 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  14. Onnela, J.-P., Chakraborti, A., Kaski, K., Kertesz, J. & Kanto, A. Dynamics of market correlations: taxonomy and portfolio analysis. Phys. Rev. E 68, 056110 (2003).

    Article  CAS  Google Scholar 

  15. Gastner, M. T. & Newman, M. E. J. The spatial structure of networks. Eur. Phys. J. B 49, 247–252 (2006).

    Article  CAS  Google Scholar 

  16. Barthelemy, M. Spatial networks. Phys. Rep. 499, 1–101 (2011). This is an authoritative review of the statistical physics of topologically complex networks embedded in space, with many examples outside neuroscience.

    Article  CAS  Google Scholar 

  17. Yook, S. H., Jeong, H. W. & Barabasi, A. L. Modeling the Internet's large-scale topology. Proc. Natl Acad. Sci. USA 99, 13382–13386 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Chklovskii, D. B. & Koulakov, A. A. Maps in the brain: what can we learn from them? Annu. Rev. Neurosci. 27, 369–392 (2004).

    Article  CAS  PubMed  Google Scholar 

  19. Kaiser, M. & Hilgetag, C. C. Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comp. Biol. 2, e95 (2006). This is a computational study demonstrating that strict minimization of wiring cost of macaque monkey and C. elegans connectomes entails an increase in their characteristic path-lengths.

    Article  CAS  Google Scholar 

  20. Achard, S. & Bullmore, E. Efficiency and cost of economical brain functional networks. PLoS Comp. Biol. 3, e17 (2007).

    Article  CAS  Google Scholar 

  21. Chklovskii, D. B. Synaptic connectivity and neuronal morphology: two sides of the same coin. Neuron 43, 609–617 (2004).

    CAS  PubMed  Google Scholar 

  22. Ramon y Cajal, S. Texture of the Nervous System of Man and Vertebrates (Oxford Univ. Press, New York, 1995).

    Google Scholar 

  23. Garcia-Lopez, P., Garcia-Marin, V. & Freire, M. The histological slides and drawings of Cajal. Front. Neuroanat. 4, 9 (2010).

    PubMed  PubMed Central  Google Scholar 

  24. Cherniak, C., Mokhtarzada, Z., Rodriguez-Estaban, R. & Changizi, K. Global optimization of cerebral cortex layout. Proc. Natl Acad. Sci. USA 101, 1081–1086 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Klyachko, V. A. & Stevens, C. F. Connectivity optimization and the positioning of cortical areas. Proc. Natl Acad. Sci. USA 100, 7937–7941 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Cuntz, H., Forstner, F., Borst, A. & Hausser, M. One rule to grow them all: a general theory of neuronal branching and its practical application. PLoS Comp. Biol. 6, e1000877 (2010).

    Article  CAS  Google Scholar 

  27. Rivera-Alba, M. et al. Wiring economy and volume exclusion determine neuronal placement in the Drosophila brain. Curr. Biol. 21, 2000–2005 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Chklovskii, D. B. Exact solution for the optimal neuronal layout problem. Neural Comput. 16, 2067–2078 (2004).

    Article  PubMed  Google Scholar 

  29. Niven, J. E. & Laughlin, S. B. Energy limitation as a selective pressure on the evolution of sensory systems. J. Exp. Biol. 211, 1792–1804 (2008).

    Article  CAS  PubMed  Google Scholar 

  30. Striedter, G. F. Principles of Brain Evolution (Sinauer, 2005).

    Google Scholar 

  31. Jerison, H. J. Evolution of the Brain and Intelligence (Academic Press, 1973).

    Google Scholar 

  32. Deacon, T. W. Rethinking mammalian brain evolution. Am. Zool. 30, 629–705 (1990).

    Article  Google Scholar 

  33. Ringo, J. L. Neuronal interconnection as a function of brain size. Brain Behav. Evol. 38, 1–6 (1991).

    Article  CAS  PubMed  Google Scholar 

  34. Zhang, K. & Sejnowski, T. J. A universal scaling law between gray matter and white matter of cerebral cortex. Proc. Natl Acad. Sci. USA 97, 5621–5626 (2000).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Changizi, M. A. Principles underlying mammalian neocortical scaling. Biol. Cybern. 84, 207–215 (2001).

    Article  CAS  PubMed  Google Scholar 

  36. Herculano-Houzel, S., Mota, B., Wong, P. Y. & Kaas, J. H. Connectivity-driven white matter scaling and folding in primate cerebral cortex. Proc. Natl Acad. Sci. USA 107, 19008–19013 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Buzsaki, G., Geisler, C., Henze, D. A. & Wang, X.-J. Circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27, 186–193 (2004).

    Article  CAS  PubMed  Google Scholar 

  38. Chen, B. L., Hall, D. H. & Chklovskii, D. B. Wiring optimization can relate neuronal structure and function. Proc. Natl Acad. Sci. USA 103, 4723–4728 (2006). This study shows that the anatomical layout (component placement) of the neurons comprising the C. elegans nervous system is near-minimal given network functionality.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Perez-Escudero, A. & De Polavieja, G. G. Optimally wired subnetwork determines neuroanatomy of Caenorhabditis elegans. Proc. Natl Acad. Sci. USA 104, 17180–17185 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Hellwig, B. A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex. Biol. Cybern. 82, 111–121 (2000).

    Article  CAS  PubMed  Google Scholar 

  41. Stepanyants, A. et al. Local potential connectivity in cat primary visual cortex. Cereb. Cortex 18, 13–28 (2008).

    Article  PubMed  Google Scholar 

  42. Averbeck, B. B. & Seo, M. The statistical neuroanatomy of frontal networks in the macaque. PLoS Comp. Biol. 4 e1000050 (2008).

    Article  CAS  Google Scholar 

  43. Markov, N. T. et al. Weight consistency specifies regularities of macaque cortical networks. Cereb. Cortex 21, 1254–1272 (2011).

    Article  CAS  PubMed  Google Scholar 

  44. Kaiser, M. & Hilgetag, C. C. Modelling the development of cortical systems networks. Neurocomputing 58, 297–302 (2004).

    Article  Google Scholar 

  45. Salvador, R. et al. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb. Cortex 15, 1332–1342 (2005).

    Article  PubMed  Google Scholar 

  46. Alexander-Bloch, A. F. et al. The anatomical distance of functional connections predicts brain network topology in health and schizophrenia. Cereb. Cortex 23 Jan 2012 (doi:10.1093/cercor/bhr388). This is a clinical study of the relationships between connection distance and functional network topology in resting state fMRI data from healthy adults and people with schizophrenia.

    Article  PubMed  PubMed Central  Google Scholar 

  47. Van Essen, D. C. A tension-based theory of morphogenesis and compact wiring in the central nervous system. Nature 385, 313–318 (1997).

    Article  CAS  PubMed  Google Scholar 

  48. Young, M. P. & Scannell, J. W. Component placement optimization in the brain. Trends Neurosci. 19, 413–414 (1996).

    Article  CAS  PubMed  Google Scholar 

  49. Attwell, D. & Laughlin, S. B. An energy budget for signaling in the grey matter of the brain. J. Cereb. Blood Flow Metab. 21, 1133–1145 (2001).

    Article  CAS  PubMed  Google Scholar 

  50. Laughlin, S. B. & Sejnowski, T. J. Communication in neuronal networks. Science 301, 1870–1874 (2003). This is a seminal review of cost constraints on the efficiency of nervous systems and their adaptability.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  51. Karbowski, J. Global and regional brain metabolic scaling and its functional consequences. BMC Biol. 5, 18 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Laughlin, S. B., van Steveninck, R. R. D. & Anderson, J. C. The metabolic cost of neural information. Nature Neurosci. 1, 36–41 (1998).

    Article  CAS  PubMed  Google Scholar 

  53. Desimone, R. Neural mechanisms for visual memory and their role in attention. Proc. Natl Acad. Sci. USA 93, 13494–13499 (1996).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Breiter, H. C. et al. Response and habituation of the human amygdala during visual processing of facial expression. Neuron 17, 875–887 (1996).

    Article  CAS  PubMed  Google Scholar 

  55. Friston, K. J. The free-energy principle: a unified brain theory? Nature Rev. Neurosci. 11, 127–138 (2010).

    Article  CAS  Google Scholar 

  56. Strelnikov, K. Neuroimaging and neuroenergetics: brain activations as information-driven reorganization of energy flows. Brain Cogn. 72, 449–456 (2010).

    Article  PubMed  Google Scholar 

  57. Kiebel, S. J. & Friston, K. J. Free energy and dendritic self-organization. Front. Syst. Neurosci. 5, 80 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  58. Honey, C. J. et al. Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl Acad. Sci. USA 106, 2035–2040 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Smith, S. M. et al. Network modelling methods for fMRI. Neuroimage 54, 875–891 (2011).

    Article  PubMed  Google Scholar 

  60. Adachi, Y. et al. Functional connectivity between anatomically unconnected areas is shaped by collective network-level effects in the macaque cortex. Cereb. Cortex 5 Sep 2011 (doi:10.1093/cercor/bhr234).

    Article  PubMed  Google Scholar 

  61. Felleman, D. J. & van Essen, D. C. Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1–47 (1991).

    Article  CAS  PubMed  Google Scholar 

  62. Scannell, J. W., Burns, G., Hilgetag, C. C., O'Neil, M. A. & Young, M. P. The connectional organization of the cortico-thalamic system of the cat. Cereb. Cortex 9, 277–299 (1999).

    Article  CAS  PubMed  Google Scholar 

  63. 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, 63–72 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Hagmann, P. et al. Mapping the structural core of human cerebral cortex. PLoS Biol. 6, 1479–1493 (2008). This comprehensive study demonstrates a broad range of nonrandom topological properties, including a medial cortical core of densely interconnected regions, in human brain anatomical networks derived from diffusion imaging data.

    Article  CAS  Google Scholar 

  65. Sporns, O., Tononi, G. & Kotter, R. The human connectome: a structural description of the human brain. PLoS Comp. Biol. 1, 245–251 (2005).

    Article  CAS  Google Scholar 

  66. Bullmore, E. T. & Bassett, D. S. Brain graphs: graphical models of the human brain connectome. Annu. Rev. Clin. Psychol. 7, 113–140 (2011).

    Article  PubMed  Google Scholar 

  67. Latora, V. & Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001).

    Article  CAS  PubMed  Google Scholar 

  68. Meunier, D., Achard, S., Morcom, A. & Bullmore, E. Age-related changes in modular organization of human brain functional networks. Neuroimage 44, 715–723 (2009).

    Article  PubMed  Google Scholar 

  69. Meunier, D., Lambiotte, R., Fornito, A., Ersche, K. D. & Bullmore, E. T. Hierarchical modularity in human brain functional networks. Front. Neuroinform. 3, 37 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  70. Chen, Z. J., He, Y., Rosa-Neto, P., Germann, J. & Evans, A. C. Revealing modular architecture of human brain structural networks by using cortical thickness from MRI. Cereb. Cortex 18, 2374–2381 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  71. He, Y. et al. Uncovering intrinsic modular organization of spontaneous brain activity in humans. PLoS ONE 4, e5226 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Eguiluz, V. M., Chialvo, D. R., Cecchi, G. A., Baliki, M. & Apkarian, A. V. Scale-free brain functional networks. Phys. Rev. Lett. 94, 018102 (2005).

    Article  CAS  PubMed  Google Scholar 

  73. Sporns, O., Honey, C. J. & Kotter, R. Identification and classification of hubs in brain networks. PLoS ONE 2, e1049 (2007).

    Article  PubMed  PubMed Central  Google Scholar 

  74. Rubinov, M. & Sporns, O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010).

    Article  PubMed  Google Scholar 

  75. Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H. & Chklovskii, D. B. Structural properties of the Caenorhabditis elegans neuronal network. PLoS Comp. Biol. 7, e1001066 (2011).

    Article  CAS  Google Scholar 

  76. Yu, S., Huang, D., Singer, W. & Nikolic, D. A small world of neuronal synchrony. Cereb. Cortex 18, 2891–2901 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  77. Kaiser, M., Hilgetag, C. C. & Kotter, R. Hierarchy and dynamics of neural networks. Front. Neuroinform. 4, 112 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  78. Sole, R. V., Valverde, S. & Rodriguez-Caso, C. Convergent evolutionary paths in biological and technological networks. Evolution 4, 415–426 (2011).

    Article  Google Scholar 

  79. Milo, R. et al. Superfamilies of evolved and designed networks. Science 303, 1538–1542 (2004).

    Article  CAS  PubMed  Google Scholar 

  80. Sporns, O., Chialvo, D. R., Kaiser, M. & Hilgetag, C. C. Organization, development and function of complex brain networks. Trends Cogn. Sci. 8, 418–425 (2004).

    Article  PubMed  Google Scholar 

  81. Bassett, D. S. & Bullmore, E. Small-world brain networks. Neuroscientist 12, 512–523 (2006).

    Article  PubMed  Google Scholar 

  82. Tononi, G. & Sporns, O. Measuring information integration. BMC Neurosci. 4, 31 (2003).

    Article  PubMed  PubMed Central  Google Scholar 

  83. Tononi, G., Sporns, O. & Edelman, G. M. A measure for brain complexity: relating functional segregation and integration in the nervous system. Proc. Natl Acad. Sci. USA 91, 5033–5037 (1994).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  84. Gallos, L. K., Makse, H. A. & Sigman, M. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. Proc. Natl Acad. Sci. USA 109, 2825–2830 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  85. Chen, Z. J., He, Y., Rosa-Neto, P., Gong, G. & Evans, A. C. Age-related alterations in the modular organization of structural cortical network by using cortical thickness from MRI. Neuroimage 56, 235–245 (2011).

    Article  PubMed  Google Scholar 

  86. Li, Y. et al. Brain anatomical network and intelligence. PLoS Comp. Biol. 5, e1000395 (2009).

    Article  CAS  Google Scholar 

  87. van den Heuvel, M. P., Stam, C. J., Kahn, R. S. & Hulshoff Pol, H. E. Efficiency of functional brain networks and intellectual performance. J. Neurosci. 29, 7619–7624 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  88. Langer, N. et al. Functional brain network efficiency predicts intelligence. Hum. Brain Mapp. 9 May 2011 (doi:10.1002/hbm.21297).

    Article  PubMed  PubMed Central  Google Scholar 

  89. Baars, B. J. The conscious access hypothesis: origins and recent evidence. Trends Cogn. Sci. 6, 47–52 (2002).

    Article  PubMed  Google Scholar 

  90. Dehaene, S. & Naccache, L. Towards a cognitive neuroscience of consciousness: basic evidence and a workspace framework. Cognition 79, 1–37 (2001).

    Article  CAS  PubMed  Google Scholar 

  91. Dehaene, S. & Changeux, J.-P. Experimental and theoretical approaches to conscious processing. Neuron 70, 200–227 (2011). This is an authoritative review of global neuronal workspace and related network theories of cognition and consciousness.

    Article  CAS  PubMed  Google Scholar 

  92. Shanahan, M. Embodiment and the Inner Life: Cognition and Consciousness in the Space of Possible Minds (Oxford Univ. Press, 2010).

    Book  Google Scholar 

  93. Rubinov, M., Sporns, O., van Leeuwen, C. & Breakspear, M. Symbiotic relationship between brain structure and dynamics. BMC Neurosci. 10, 55 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  94. Simon, H. A. The architecture of complexity. Proc. Am. Phil. Soc. 106, 467–482 (1962).

    Google Scholar 

  95. Robinson, P. A., Henderson, J. A., Matar, E., Riley, P. & Gray, R. T. Dynamical reconnection and stability constraints on cortical network architecture. Phys. Rev. Lett. 103, 4 (2009).

    Google Scholar 

  96. Rubinov, M., Sporns, O., Thivierge, J. P. & Breakspear, M. Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons. PLoS Comp. Biol. 7, e1002038 (2011). This computational model shows that small-world and other realistically non-random topological properties of brain networks favour the emergence of complex dynamics compatible with a self-organized state of criticality.

    Article  CAS  Google Scholar 

  97. Beggs, J. M. The criticality hypothesis: how local cortical networks might optimize information processing. Phil. Trans. R. Soc. A 366, 329–343 (2008).

    Article  PubMed  Google Scholar 

  98. Chialvo, D. R. Emergent complex neural dynamics. Nature Phys. 6, 744–750 (2010).

    Article  CAS  Google Scholar 

  99. Petermann, T. et al. Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proc. Natl Acad. Sci. USA 106, 15921–15926 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  100. Shew, W. L., Yang, H., Petermann, T., Roy, R. & Plenz, D. Neuronal avalanches imply maximum dynamic range in cortical networks at criticality. J. Neurosci. 29, 15595–15600 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. Kitzbichler, M. G., Smith, M. L., Christensen, S. R. & Bullmore, E. Broadband criticality of human brain network synchronization. PLoS Comp. Biol. 5, e1000314 (2009).

    Article  CAS  Google Scholar 

  102. Swanson, L. W. Brain Architecture (Oxford Univ. Press, 2007).

    Google Scholar 

  103. Krubitzer, L. The magnificent compromise: cortical field evolution in mammals. Neuron 56, 201–208 (2007).

    Article  CAS  PubMed  Google Scholar 

  104. Kaufman, A., Dror, G., Meilijson, I. & Ruppin, E. Gene expression of Caenorhabditis elegans neurons carries information on their synaptic connectivity. PLoS Comp. Biol. 2, 1561–1567 (2006).

    Article  CAS  Google Scholar 

  105. French, L. & Pavlidis, P. Relationships between gene expression and brain wiring in the adult rodent brain. PLoS Comp. Biol. 7, e1001049 (2011).

    Article  CAS  Google Scholar 

  106. Henderson, J. A. & Robinson, P. A. Geometric effects on complex network structure in the cortex. Phys. Rev. Lett. 107, 018102 (2011).

    Article  CAS  PubMed  Google Scholar 

  107. Meunier, D., Lambiotte, R. & Bullmore, E. T. Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4, 200 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  108. Ahn, Y. Y., Jeong, H. & Kim, B. J. Wiring cost in the organization of a biological neuronal network. Physica A 367, 531–537 (2006).

    Article  Google Scholar 

  109. Bassett, D. S. et al. Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comp. Biol. 6, e1000748 (2010). This paper describes a translational study that uses the science of VLSI computer circuits to show that brain circuits are as economically embedded as they can be, given that the topological dimension of brain circuits is greater than the three-dimensionality of the brain space.

    Article  CAS  Google Scholar 

  110. Bassett, D. S. et al. Cognitive fitness of cost-efficient brain functional networks. Proc. Natl Acad. Sci. USA 106, 11747–11752 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  112. Chang, C. & Glover, G. H. Time-frequency dynamics of resting-state brain connectivity measured with fMRI. Neuroimage 50, 81–98 (2010).

    Article  PubMed  Google Scholar 

  113. Palva, J. M., Monto, S., Kulashekhar, S. & Palva, S. Neuronal synchrony reveals working memory networks and predicts individual memory capacity. Proc. Natl Acad. Sci. USA 107, 7580–7585 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  114. Nicol, R. M. et al. Fast reconfiguration of high frequency brain networks in response to surprising changes in auditory input. J. Neurophysiol. 107, 1421–1430 (2012).

    Article  PubMed  Google Scholar 

  115. Bassett, D. S. et al. Dynamic reconfiguration of human brain networks during learning. Proc. Natl Acad. Sci. USA 108, 7641–7646 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  116. Kitzbichler, M. G., Henson, R. N. A., Smith, M. L., Nathan, P. J. & Bullmore, E. T. Cognitive effort drives workspace configuration of human brain functional networks. J. Neurosci. 31, 8259–8270 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  117. Hagmann, P. et al. White matter maturation reshapes structural connectivity in the late developing human brain. Proc. Natl Acad. Sci. USA 107, 19067–19072 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  118. Fair, D. A. et al. Functional brain networks develop from a “local to distributed” organization. PLoS Comp. Biol. 5, e1000381 (2009).

    Article  CAS  Google Scholar 

  119. Supekar, K., Musen, M. & Menon, V. Development of large-scale functional brain networks in children. PLoS Biol. 7, e1000157 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  120. Power, J. D., Barnes, K. A., Snyder, A. Z., Schlaggar, B. L. & Petersen, S. E. Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion. Neuroimage 59, 2142–2154 (2012).

    Article  PubMed  Google Scholar 

  121. Bassett, D. S. & Bullmore, E. T. Human brain networks in health and disease. Curr. Opin. Neurol. 22, 340–347 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  122. Fornito, A. & Bullmore, E. T. What can spontaneous fluctuations of the blood oxygenation-level-dependent signal tell us about psychiatric disorders? Curr. Opin. Psychiatry. 23, 239–249 (2010).

    Article  PubMed  Google Scholar 

  123. Yao, Z. et al. Abnormal cortical networks in mild cognitive impairment and Alzheimer's disease. PLoS Comp. Biol. 6, e1001006 (2010).

    Article  CAS  Google Scholar 

  124. Lo, C. Y. et al. Diffusion tensor tractography reveals abnormal topological organization in structural cortical networks in Alzheimer's disease. J. Neurosci. 30, 16876–16885 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  125. Stam, C. J., Jones, B. F., Nolte, G., Breakspear, M. & Scheltens, P. Small-world networks and functional connectivity in Alzheimer's disease. Cereb. Cortex 17, 92–99 (2007).

    Article  CAS  PubMed  Google Scholar 

  126. He, Y., Chen, Z. & Evans, A. C. Structural insights into aberrant topological patterns of large-scale cortical networks in Alzheimer's disease. J. Neurosci. 28, 4756–4766 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  127. Buckner, R. L. et al. Cortical hubs revealed by intrinsic functional connectivity: mapping, assessment of stability, and relation to Alzheimer's disease. J. Neurosci. 29, 1860–1873 (2009). This paper discusses a clinical study linking the topological importance of hubs in functional networks to their metabolic costs and hence to their vulnerability to pathological damage in Alzheimer's disease.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  128. He, Y. et al. Impaired small-world efficiency in structural cortical networks in multiple sclerosis associated with white matter lesion load. Brain 132, 3366–3379 (2009). This clinical study links radiological measures of white-matter lesion load to impairments of topological efficiency of anatomical networks in patients with a demyelinating disorder.

    Article  PubMed  PubMed Central  Google Scholar 

  129. Zamora-Lopez, G., Zhou, C. & Kurths, J. Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks. Front. Neuroinform. 4, 1 (2010).

    PubMed  PubMed Central  Google Scholar 

  130. van den Heuvel, M. P. & Sporns, O. Rich club organization of the human connectome. J. Neurosci. 31, 15775–15786 (2011). This study shows that human brain networks have a rich club organization, consisting of a subset of highly interconnected hub nodes that are likely to be important for integrated processing.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  131. Honey, C. J. & Sporns, O. Dynamical consequences of lesions in cortical networks. Hum. Brain Mapp. 29, 802–809 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  132. Alstott, J., Breakspear, M., Hagmann, P., Cammoun, L. & Sporns, O. Modeling the impact of lesions in the human brain. PLoS Comp. Biol. 5, e1000408 (2009).

    Article  CAS  Google Scholar 

  133. Liu, Y. et al. Disrupted small-world networks in schizophrenia. Brain 131, 945–961 (2008).

    Article  PubMed  Google Scholar 

  134. Alexander-Bloch, A. F. et al. Disrupted modularity and local connectivity of brain functional networks in childhood onset schizophrenia. Front. Syst. Neurosci. 4, 147 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  135. Lynall, M. E. et al. Functional connectivity and brain networks in schizophrenia. J. Neurosci. 30, 9477–9487 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  136. Rubinov, M. et al. Small-world properties of nonlinear brain activity in schizophrenia. Hum. Brain Mapp. 30, 403–416 (2009).

    Article  PubMed  Google Scholar 

  137. Lord, L. D. et al. Characterization of the anterior cingulate's role in the at-risk mental state using graph theory. Neuroimage 56, 1531–1539 (2011).

    Article  PubMed  Google Scholar 

  138. Fornito, A., Zalesky, A., Pantelis, C. & Bullmore, E. Schizophrenia, neuroimaging and connectomics. Neuroimage 24 Feb 2012 (doi:10.1016/j.neuroimage/2011/12/090).

  139. van den Heuvel, M. P., Mandl, R. C. W., Stam, C. J., Kahn, R. S. & Hulshoff Pol, H. E. Aberrant frontal and temporal complex network structure in schizophrenia: a graph theoretical analysis. J. Neurosci. 30, 15915–15926 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  140. Zalesky, A. et al. Disrupted axonal fiber connectivity in schizophrenia. Biol. Psychiatry 69, 80–89 (2011).

    Article  PubMed  Google Scholar 

  141. Bassett, D. S. et al. Hierarchical organization of human cortical networks in health and schizophrenia. J. Neurosci. 28, 9239–9248 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  142. Kaiser, M., Hilgetag, C. C. & van Ooyen, A. A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions. Cereb. Cortex 19, 3001–3010 (2009).

    Article  PubMed  Google Scholar 

  143. Vértes, P. E. et al. Simple models of human brain functional networks. Proc. Natl Acad. Sci. USA 30 Mar 2012 (doi:10.1073/pnas.1111738109).

    Article  CAS  Google Scholar 

  144. Le Gros Clark, W. in Essays on Growth and Form 1–23 (Oxford Univ. Press 1945).

    Google Scholar 

  145. Welker, W. in Cereb Cortex (eds Jones, E. & Peters, A.) 3–136 (Plenum Press, 1990).

    Book  Google Scholar 

  146. Scannell, J. W. Determining cortical landscapes. Nature 386, 452–452 (1997).

    Article  CAS  PubMed  Google Scholar 

  147. Rademacher, J. et al. Probabilistic mapping and volume measurement of human primary auditory cortex. Neuroimage 13, 669–683 (2001).

    Article  CAS  PubMed  Google Scholar 

  148. Hilgetag, C. C. & Barbas, H. Role of mechanical factors in the morphology of the primate cerebral cortex. PLoS Comp. Biol. 2, e22 (2006).

    Article  CAS  Google Scholar 

  149. Van Essen, D. C. et al. Symmetry of cortical folding abnormalities in Williams syndrome revealed by surface-based analyses. J. Neurosci. 26, 5470–5483 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  150. Kirschner, M. & Gerhart, J. Evolvability. Proc. Natl Acad. Sci. USA 95, 8420–8427 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  151. Newman, M. E. J. Modularity and community structure in networks. Proc. Natl Acad. Sci. USA 103, 8577–8582 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  152. Lipson, H., Pollack, J. B. & Suh, N. P. On the origin of modular variation. Evolution 56, 1549–1556 (2002).

    Article  PubMed  Google Scholar 

  153. Kashtan, N. & Alon, U. Spontaneous evolution of modularity and network motifs. Proc. Natl Acad. Sci. USA 102, 13773–13778 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  154. Variano, E. A., McCoy, J. H. & Lipson, H. Networks, dynamics, and modularity. Phys. Rev. Lett. 92, 188701 (2004).

    Article  CAS  PubMed  Google Scholar 

  155. Guimera, R., Mossa, S., Turtschi, A. & Amaral, L. A. N. The worldwide air transportation network: anomalous centrality, community structure, and cities' global roles. Proc. Natl Acad. Sci. USA 102, 7794–7799 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  156. Zamora-Lopez, G., Zhou, C. S. & Kurths, J. Graph analysis of cortical networks reveals complex anatomical communication substrate. Chaos 19, 015117 (2009).

    Article  PubMed  Google Scholar 

  157. Zamora-Lopez, G., Zhou, C. & Kurths, J. Exploring brain function from anatomical connectivity. Front. Neurosci. 5, 83 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  158. Roth, G. & Dicke, U. Evolution of the brain and intelligence. Trends Cogn. Sci. 9, 250–257 (2005).

    Article  PubMed  Google Scholar 

  159. Changizi, M. A. in The Evolution of Nervous Systems in Mammals (eds Kaas, J. H. & Krubitzer, L.) 181–187 (Academic Press, 2006).

    Google Scholar 

  160. Bush, E. C. & Allman, J. M. The scaling of white matter to gray matter in cerebellum and neocortex. Brain Behav. Evol. 61, 1–5 (2003).

    Article  PubMed  Google Scholar 

  161. Vaishnavi, S. N. et al. Regional aerobic glycolysis in the human brain. Proc. Natl Acad. Sci. USA 107, 17757–17762 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  162. Buckner, R. L. et al. Molecular, structural, and functional characterization of Alzheimer's disease: evidence for a relationship between default activity, amyloid, and memory. J. Neurosci. 25, 7709–7717 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  163. Buckner, R. L., Andrews-Hanna, J. R., Schacter, D. L. The brain's default network: anatomy, function, and relevance to disease. Ann. N.Y. Acad. Sci. 1124, 1–38 (2008).

    Article  PubMed  Google Scholar 

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Acknowledgements

The Behavioural and Clinical Neuroscience Institute, University of Cambridge, is supported by the Medical Research Council (UK) and the Wellcome Trust.

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Correspondence to Ed Bullmore or Olaf Sporns.

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Ed Bullmore is a part-time employee and stockholder of GlaxoSmithKline. Olaf Sporns declares no competing financial interests.

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Glossary

Graphs

Simple models of a system that are based on a set of nodes and the edges between them. The nodes represent agents or elements, and the edges represent interactions or connections between nodes.

Topology

Applied to a network, the layout pattern of interconnections, defined in terms of the relations of nodes and edges.

Robustness

The degree to which the topological properties of a network are resilient to 'lesions' such as the removal of nodes or edges.

Hub

A topologically important or central node, as defined by one of several possible measures of centrality, including degree centrality (number of edges) or betweenness centrality.

Wiring cost

The fixed cost of making anatomical connections between neurons, often approximated by the wiring volume of anatomical connections.

Efficiency

A topological measure of the reciprocal or inverse of the path length between nodes. In brain networks, global efficiency is often used as a measure of the overall capacity for parallel information transfer and integrated processing.

Economy

Applied to brain network organization, economy refers to the careful management of resources in the service of delivering robust and efficient performance.

Allometric scaling

Allometric scaling concerns the relationships between body size (scale) and other anatomical, functional or metabolic properties of organisms. These scaling relationships are often described by power laws.

Connection distances

Spatial measures that describe the physical distance between nodes that are connected by an edge in the network; often approximated as the Euclidean distance between nodes.

Functional connectivity

Statistical association — for example, significant correlations — between neurophysiological measurements recorded from anatomically distinct neurons or regions at several time points.

Edges

In a brain graph, an edge between nodes (regions or neurons) indicates that the nodes are anatomically or functionally connected.

Path length

A measure of network topology. In a binary graph, the path length between two nodes is the minimum number of edges that must be traversed to get from one node to another.

Sparse coding

A type of neural coding that represents information by the activation of a small subset of the available neurons and/or by activation of neurons over a brief instant of time.

Connection density

A topological measure that describes the number of edges in a network as a proportion of the maximum possible number of edges, namely (N2N)/2 for an undirected network of N nodes.

Small world

A term used to describe complex networks that have a combination of both random and regular topological properties; that is, high efficiency (short path-length) and high clustering, respectively.

Clustering

A measure of that captures the 'cliquishness' of a local neighbourhood, based on the number of triangular connections between groups of three nodes.

Community structure

The sub-global organization of a complex network. Modularity is an example of community structure, but not all network communities are simply modular.

Heavy-tailed degree distributions

A term that is generally used to mean that the proportion of high-degree nodes (nodes with a large number of edges connecting them to other nodes (hubs)) is greater than that in random graphs.

Centrality

A topological measure of the importance or influence of a node or edge for network organization.

Critical dynamics

If a system is dynamically on the cusp of a phase transition between random and regular dynamics, it is said to be in a critical state or demonstrating critical dynamics.

Simulated annealing

A computer algorithm used to find a good approximation to the global optimum of a function over a large search space.

Connector hubs

Hubs that mediate a high proportion of inter-modular (often long-distance) connections.

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Bullmore, E., Sporns, O. The economy of brain network organization. Nat Rev Neurosci 13, 336–349 (2012). https://doi.org/10.1038/nrn3214

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