The economy of brain network organization (original) (raw)

• Albert, R. & Barabasi, A. L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002).
  Article Google Scholar
• Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440–442 (1998).
  Article CAS PubMed Google Scholar
• 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
• Barrat, A., Barthelemy, M. & Vespignani, A. Dynamical Processes on Complex Networks (Cambridge Univ. Press, 2008).
  Book Google Scholar
• Sporns, O. Networks of the Brain (MIT Press, 2011).
  Google Scholar
• 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
• 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
• 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
• Vespignani, A. Modelling dynamical processes in complex socio-technical systems. Nature Phys. 8, 32–39 (2012).
  Article CAS Google Scholar
• 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
• 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
• 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
• 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
• 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
• Gastner, M. T. & Newman, M. E. J. The spatial structure of networks. Eur. Phys. J. B 49, 247–252 (2006).
  Article CAS Google Scholar
• 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
• 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
• 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
• 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
• Achard, S. & Bullmore, E. Efficiency and cost of economical brain functional networks. PLoS Comp. Biol. 3, e17 (2007).
  Article CAS Google Scholar
• Chklovskii, D. B. Synaptic connectivity and neuronal morphology: two sides of the same coin. Neuron 43, 609–617 (2004).
  CAS PubMed Google Scholar
• Ramon y Cajal, S. Texture of the Nervous System of Man and Vertebrates (Oxford Univ. Press, New York, 1995).
  Google Scholar
• 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
• 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
• 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
• 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
• 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
• Chklovskii, D. B. Exact solution for the optimal neuronal layout problem. Neural Comput. 16, 2067–2078 (2004).
  Article PubMed Google Scholar
• 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
• Striedter, G. F. Principles of Brain Evolution (Sinauer, 2005).
  Google Scholar
• Jerison, H. J. Evolution of the Brain and Intelligence (Academic Press, 1973).
  Google Scholar
• Deacon, T. W. Rethinking mammalian brain evolution. Am. Zool. 30, 629–705 (1990).
  Article Google Scholar
• Ringo, J. L. Neuronal interconnection as a function of brain size. Brain Behav. Evol. 38, 1–6 (1991).
  Article CAS PubMed Google Scholar
• 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
• Changizi, M. A. Principles underlying mammalian neocortical scaling. Biol. Cybern. 84, 207–215 (2001).
  Article CAS PubMed Google Scholar
• 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
• 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
• 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
• 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
• 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
• Stepanyants, A. et al. Local potential connectivity in cat primary visual cortex. Cereb. Cortex 18, 13–28 (2008).
  Article PubMed Google Scholar
• Averbeck, B. B. & Seo, M. The statistical neuroanatomy of frontal networks in the macaque. PLoS Comp. Biol. 4 e1000050 (2008).
  Article CAS Google Scholar
• Markov, N. T. et al. Weight consistency specifies regularities of macaque cortical networks. Cereb. Cortex 21, 1254–1272 (2011).
  Article CAS PubMed Google Scholar
• Kaiser, M. & Hilgetag, C. C. Modelling the development of cortical systems networks. Neurocomputing 58, 297–302 (2004).
  Article Google Scholar
• Salvador, R. et al. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb. Cortex 15, 1332–1342 (2005).
  Article PubMed Google Scholar
• 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
• 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
• Young, M. P. & Scannell, J. W. Component placement optimization in the brain. Trends Neurosci. 19, 413–414 (1996).
  Article CAS PubMed Google Scholar
• 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
• 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
• Karbowski, J. Global and regional brain metabolic scaling and its functional consequences. BMC Biol. 5, 18 (2007).
  Article CAS PubMed PubMed Central Google Scholar
• 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
• 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
• 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
• Friston, K. J. The free-energy principle: a unified brain theory? Nature Rev. Neurosci. 11, 127–138 (2010).
  Article CAS Google Scholar
• Strelnikov, K. Neuroimaging and neuroenergetics: brain activations as information-driven reorganization of energy flows. Brain Cogn. 72, 449–456 (2010).
  Article PubMed Google Scholar
• Kiebel, S. J. & Friston, K. J. Free energy and dendritic self-organization. Front. Syst. Neurosci. 5, 80 (2011).
  Article PubMed PubMed Central Google Scholar
• 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
• Smith, S. M. et al. Network modelling methods for fMRI. Neuroimage 54, 875–891 (2011).
  Article PubMed Google Scholar
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Latora, V. & Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001).
  Article CAS PubMed Google Scholar
• 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
• 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
• 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
• 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
• 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
• 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
• Rubinov, M. & Sporns, O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010).
  Article PubMed Google Scholar
• 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
• 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
• Kaiser, M., Hilgetag, C. C. & Kotter, R. Hierarchy and dynamics of neural networks. Front. Neuroinform. 4, 112 (2010).
  Article PubMed PubMed Central Google Scholar
• Sole, R. V., Valverde, S. & Rodriguez-Caso, C. Convergent evolutionary paths in biological and technological networks. Evolution 4, 415–426 (2011).
  Article Google Scholar
• Milo, R. et al. Superfamilies of evolved and designed networks. Science 303, 1538–1542 (2004).
  Article CAS PubMed Google Scholar
• 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
• Bassett, D. S. & Bullmore, E. Small-world brain networks. Neuroscientist 12, 512–523 (2006).
  Article PubMed Google Scholar
• Tononi, G. & Sporns, O. Measuring information integration. BMC Neurosci. 4, 31 (2003).
  Article PubMed PubMed Central Google Scholar
• 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
• 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
• 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
• Li, Y. et al. Brain anatomical network and intelligence. PLoS Comp. Biol. 5, e1000395 (2009).
  Article CAS Google Scholar
• 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
• 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
• Baars, B. J. The conscious access hypothesis: origins and recent evidence. Trends Cogn. Sci. 6, 47–52 (2002).
  Article PubMed Google Scholar
• 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
• 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
• Shanahan, M. Embodiment and the Inner Life: Cognition and Consciousness in the Space of Possible Minds (Oxford Univ. Press, 2010).
  Book Google Scholar
• 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
• Simon, H. A. The architecture of complexity. Proc. Am. Phil. Soc. 106, 467–482 (1962).
  Google Scholar
• 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
• 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
• 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
• Chialvo, D. R. Emergent complex neural dynamics. Nature Phys. 6, 744–750 (2010).
  Article CAS Google Scholar
• 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
• 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
• 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
• Swanson, L. W. Brain Architecture (Oxford Univ. Press, 2007).
  Google Scholar
• Krubitzer, L. The magnificent compromise: cortical field evolution in mammals. Neuron 56, 201–208 (2007).
  Article CAS PubMed Google Scholar
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Liu, Y. et al. Disrupted small-world networks in schizophrenia. Brain 131, 945–961 (2008).
  Article PubMed Google Scholar
• 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
• 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
• Rubinov, M. et al. Small-world properties of nonlinear brain activity in schizophrenia. Hum. Brain Mapp. 30, 403–416 (2009).
  Article PubMed Google Scholar
• 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
• Fornito, A., Zalesky, A., Pantelis, C. & Bullmore, E. Schizophrenia, neuroimaging and connectomics. Neuroimage 24 Feb 2012 (doi:10.1016/j.neuroimage/2011/12/090).
• 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
• Zalesky, A. et al. Disrupted axonal fiber connectivity in schizophrenia. Biol. Psychiatry 69, 80–89 (2011).
  Article PubMed Google Scholar
• 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
• 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
• 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
• Le Gros Clark, W. in Essays on Growth and Form 1–23 (Oxford Univ. Press 1945).
  Google Scholar
• Welker, W. in Cereb Cortex (eds Jones, E. & Peters, A.) 3–136 (Plenum Press, 1990).
  Book Google Scholar
• Scannell, J. W. Determining cortical landscapes. Nature 386, 452–452 (1997).
  Article CAS PubMed Google Scholar
• Rademacher, J. et al. Probabilistic mapping and volume measurement of human primary auditory cortex. Neuroimage 13, 669–683 (2001).
  Article CAS PubMed Google Scholar
• 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
• 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
• Kirschner, M. & Gerhart, J. Evolvability. Proc. Natl Acad. Sci. USA 95, 8420–8427 (1998).
  Article CAS PubMed PubMed Central Google Scholar
• 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
• Lipson, H., Pollack, J. B. & Suh, N. P. On the origin of modular variation. Evolution 56, 1549–1556 (2002).
  Article PubMed Google Scholar
• 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
• Variano, E. A., McCoy, J. H. & Lipson, H. Networks, dynamics, and modularity. Phys. Rev. Lett. 92, 188701 (2004).
  Article CAS PubMed Google Scholar
• 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
• 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
• Zamora-Lopez, G., Zhou, C. & Kurths, J. Exploring brain function from anatomical connectivity. Front. Neurosci. 5, 83 (2011).
  Article PubMed PubMed Central Google Scholar
• Roth, G. & Dicke, U. Evolution of the brain and intelligence. Trends Cogn. Sci. 9, 250–257 (2005).
  Article PubMed Google Scholar
• Changizi, M. A. in The Evolution of Nervous Systems in Mammals (eds Kaas, J. H. & Krubitzer, L.) 181–187 (Academic Press, 2006).
  Google Scholar
• 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
• 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
• 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
• 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