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.
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.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 14 July 2023
Dynamic network properties of the superior temporal gyrus mediate the impact of brain age gap on chronic aphasia severity
Communications Biology Open Access 14 July 2023
Pathophysiology and probable etiology of cerebral small vessel disease in vascular dementia and Alzheimer’s disease
Molecular Neurodegeneration Open Access 11 July 2023
Subscribe to this journal
Receive 12 print issues and online access
$189.00 per year
only $15.75 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Albert, R. & Barabasi, A. L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002).
Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440–442 (1998).
Bullmore, E. & Sporns, O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Rev. Neurosci. 10, 186–198 (2009).
Barrat, A., Barthelemy, M. & Vespignani, A. Dynamical Processes on Complex Networks (Cambridge Univ. Press, 2008).
Sporns, O. Networks of the Brain (MIT Press, 2011).
Vidal, M., Cusick, M. E. & Barabasi, A. L. Interactome networks and human disease. Cell 144, 986–998 (2011).
Barabasi, A. L. & Oltvai, Z. N. Network biology: understanding the cell's functional organization. Nature Rev. Genet. 5, 101–113 (2004).
Li, S. et al. A map of the interactome network of the metazoan C. elegans. Science 303, 540–543 (2004).
Vespignani, A. Modelling dynamical processes in complex socio-technical systems. Nature Phys. 8, 32–39 (2012).
Barrat, A., Barthelemy, M. & Vespignani, A. The effects of spatial constraints on the evolution of weighted complex networks. J. Stat. Mech. 2005, P05003 (2005).
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).
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).
Vertes, P. E. et al. Topological isomorphisms of human brain and financial networks. Front. Syst. Neurosci. 5, 75 (2011).
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).
Gastner, M. T. & Newman, M. E. J. The spatial structure of networks. Eur. Phys. J. B 49, 247–252 (2006).
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.
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).
Chklovskii, D. B. & Koulakov, A. A. Maps in the brain: what can we learn from them? Annu. Rev. Neurosci. 27, 369–392 (2004).
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.
Achard, S. & Bullmore, E. Efficiency and cost of economical brain functional networks. PLoS Comp. Biol. 3, e17 (2007).
Chklovskii, D. B. Synaptic connectivity and neuronal morphology: two sides of the same coin. Neuron 43, 609–617 (2004).
Ramon y Cajal, S. Texture of the Nervous System of Man and Vertebrates (Oxford Univ. Press, New York, 1995).
Garcia-Lopez, P., Garcia-Marin, V. & Freire, M. The histological slides and drawings of Cajal. Front. Neuroanat. 4, 9 (2010).
Cherniak, C., Mokhtarzada, Z., Rodriguez-Estaban, R. & Changizi, K. Global optimization of cerebral cortex layout. Proc. Natl Acad. Sci. USA 101, 1081–1086 (2004).
Klyachko, V. A. & Stevens, C. F. Connectivity optimization and the positioning of cortical areas. Proc. Natl Acad. Sci. USA 100, 7937–7941 (2003).
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).
Rivera-Alba, M. et al. Wiring economy and volume exclusion determine neuronal placement in the Drosophila brain. Curr. Biol. 21, 2000–2005 (2011).
Chklovskii, D. B. Exact solution for the optimal neuronal layout problem. Neural Comput. 16, 2067–2078 (2004).
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).
Striedter, G. F. Principles of Brain Evolution (Sinauer, 2005).
Jerison, H. J. Evolution of the Brain and Intelligence (Academic Press, 1973).
Deacon, T. W. Rethinking mammalian brain evolution. Am. Zool. 30, 629–705 (1990).
Ringo, J. L. Neuronal interconnection as a function of brain size. Brain Behav. Evol. 38, 1–6 (1991).
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).
Changizi, M. A. Principles underlying mammalian neocortical scaling. Biol. Cybern. 84, 207–215 (2001).
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).
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).
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.
Perez-Escudero, A. & De Polavieja, G. G. Optimally wired subnetwork determines neuroanatomy of Caenorhabditis elegans. Proc. Natl Acad. Sci. USA 104, 17180–17185 (2007).
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).
Stepanyants, A. et al. Local potential connectivity in cat primary visual cortex. Cereb. Cortex 18, 13–28 (2008).
Averbeck, B. B. & Seo, M. The statistical neuroanatomy of frontal networks in the macaque. PLoS Comp. Biol. 4 e1000050 (2008).
Markov, N. T. et al. Weight consistency specifies regularities of macaque cortical networks. Cereb. Cortex 21, 1254–1272 (2011).
Kaiser, M. & Hilgetag, C. C. Modelling the development of cortical systems networks. Neurocomputing 58, 297–302 (2004).
Salvador, R. et al. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb. Cortex 15, 1332–1342 (2005).
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.
Van Essen, D. C. A tension-based theory of morphogenesis and compact wiring in the central nervous system. Nature 385, 313–318 (1997).
Young, M. P. & Scannell, J. W. Component placement optimization in the brain. Trends Neurosci. 19, 413–414 (1996).
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).
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.
Karbowski, J. Global and regional brain metabolic scaling and its functional consequences. BMC Biol. 5, 18 (2007).
Laughlin, S. B., van Steveninck, R. R. D. & Anderson, J. C. The metabolic cost of neural information. Nature Neurosci. 1, 36–41 (1998).
Desimone, R. Neural mechanisms for visual memory and their role in attention. Proc. Natl Acad. Sci. USA 93, 13494–13499 (1996).
Breiter, H. C. et al. Response and habituation of the human amygdala during visual processing of facial expression. Neuron 17, 875–887 (1996).
Friston, K. J. The free-energy principle: a unified brain theory? Nature Rev. Neurosci. 11, 127–138 (2010).
Strelnikov, K. Neuroimaging and neuroenergetics: brain activations as information-driven reorganization of energy flows. Brain Cogn. 72, 449–456 (2010).
Kiebel, S. J. & Friston, K. J. Free energy and dendritic self-organization. Front. Syst. Neurosci. 5, 80 (2011).
Honey, C. J. et al. Predicting human resting-state functional connectivity from structural connectivity. Proc. Natl Acad. Sci. USA 106, 2035–2040 (2009).
Smith, S. M. et al. Network modelling methods for fMRI. Neuroimage 54, 875–891 (2011).
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).
Felleman, D. J. & van Essen, D. C. Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1–47 (1991).
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).
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).
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.
Sporns, O., Tononi, G. & Kotter, R. The human connectome: a structural description of the human brain. PLoS Comp. Biol. 1, 245–251 (2005).
Bullmore, E. T. & Bassett, D. S. Brain graphs: graphical models of the human brain connectome. Annu. Rev. Clin. Psychol. 7, 113–140 (2011).
Latora, V. & Marchiori, M. Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001).
Meunier, D., Achard, S., Morcom, A. & Bullmore, E. Age-related changes in modular organization of human brain functional networks. Neuroimage 44, 715–723 (2009).
Meunier, D., Lambiotte, R., Fornito, A., Ersche, K. D. & Bullmore, E. T. Hierarchical modularity in human brain functional networks. Front. Neuroinform. 3, 37 (2009).
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).
He, Y. et al. Uncovering intrinsic modular organization of spontaneous brain activity in humans. PLoS ONE 4, e5226 (2009).
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).
Sporns, O., Honey, C. J. & Kotter, R. Identification and classification of hubs in brain networks. PLoS ONE 2, e1049 (2007).
Rubinov, M. & Sporns, O. Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52, 1059–1069 (2010).
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).
Yu, S., Huang, D., Singer, W. & Nikolic, D. A small world of neuronal synchrony. Cereb. Cortex 18, 2891–2901 (2008).
Kaiser, M., Hilgetag, C. C. & Kotter, R. Hierarchy and dynamics of neural networks. Front. Neuroinform. 4, 112 (2010).
Sole, R. V., Valverde, S. & Rodriguez-Caso, C. Convergent evolutionary paths in biological and technological networks. Evolution 4, 415–426 (2011).
Milo, R. et al. Superfamilies of evolved and designed networks. Science 303, 1538–1542 (2004).
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).
Bassett, D. S. & Bullmore, E. Small-world brain networks. Neuroscientist 12, 512–523 (2006).
Tononi, G. & Sporns, O. Measuring information integration. BMC Neurosci. 4, 31 (2003).
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).
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).
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).
Li, Y. et al. Brain anatomical network and intelligence. PLoS Comp. Biol. 5, e1000395 (2009).
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).
Langer, N. et al. Functional brain network efficiency predicts intelligence. Hum. Brain Mapp. 9 May 2011 (doi:10.1002/hbm.21297).
Baars, B. J. The conscious access hypothesis: origins and recent evidence. Trends Cogn. Sci. 6, 47–52 (2002).
Dehaene, S. & Naccache, L. Towards a cognitive neuroscience of consciousness: basic evidence and a workspace framework. Cognition 79, 1–37 (2001).
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.
Shanahan, M. Embodiment and the Inner Life: Cognition and Consciousness in the Space of Possible Minds (Oxford Univ. Press, 2010).
Rubinov, M., Sporns, O., van Leeuwen, C. & Breakspear, M. Symbiotic relationship between brain structure and dynamics. BMC Neurosci. 10, 55 (2009).
Simon, H. A. The architecture of complexity. Proc. Am. Phil. Soc. 106, 467–482 (1962).
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).
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.
Beggs, J. M. The criticality hypothesis: how local cortical networks might optimize information processing. Phil. Trans. R. Soc. A 366, 329–343 (2008).
Chialvo, D. R. Emergent complex neural dynamics. Nature Phys. 6, 744–750 (2010).
Petermann, T. et al. Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proc. Natl Acad. Sci. USA 106, 15921–15926 (2009).
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).
Kitzbichler, M. G., Smith, M. L., Christensen, S. R. & Bullmore, E. Broadband criticality of human brain network synchronization. PLoS Comp. Biol. 5, e1000314 (2009).
Swanson, L. W. Brain Architecture (Oxford Univ. Press, 2007).
Krubitzer, L. The magnificent compromise: cortical field evolution in mammals. Neuron 56, 201–208 (2007).
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).
French, L. & Pavlidis, P. Relationships between gene expression and brain wiring in the adult rodent brain. PLoS Comp. Biol. 7, e1001049 (2011).
Henderson, J. A. & Robinson, P. A. Geometric effects on complex network structure in the cortex. Phys. Rev. Lett. 107, 018102 (2011).
Meunier, D., Lambiotte, R. & Bullmore, E. T. Modular and hierarchically modular organization of brain networks. Front. Neurosci. 4, 200 (2010).
Ahn, Y. Y., Jeong, H. & Kim, B. J. Wiring cost in the organization of a biological neuronal network. Physica A 367, 531–537 (2006).
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.
Bassett, D. S. et al. Cognitive fitness of cost-efficient brain functional networks. Proc. Natl Acad. Sci. USA 106, 11747–11752 (2009).
Fornito, A. et al. Genetic influences on cost-efficient organization of human cortical functional networks. J. Neurosci. 31, 3261–3270 (2011).
Chang, C. & Glover, G. H. Time-frequency dynamics of resting-state brain connectivity measured with fMRI. Neuroimage 50, 81–98 (2010).
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).
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).
Bassett, D. S. et al. Dynamic reconfiguration of human brain networks during learning. Proc. Natl Acad. Sci. USA 108, 7641–7646 (2011).
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).
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).
Fair, D. A. et al. Functional brain networks develop from a “local to distributed” organization. PLoS Comp. Biol. 5, e1000381 (2009).
Supekar, K., Musen, M. & Menon, V. Development of large-scale functional brain networks in children. PLoS Biol. 7, e1000157 (2009).
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).
Bassett, D. S. & Bullmore, E. T. Human brain networks in health and disease. Curr. Opin. Neurol. 22, 340–347 (2009).
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).
Yao, Z. et al. Abnormal cortical networks in mild cognitive impairment and Alzheimer's disease. PLoS Comp. Biol. 6, e1001006 (2010).
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).
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).
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).
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.
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.
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).
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.
Honey, C. J. & Sporns, O. Dynamical consequences of lesions in cortical networks. Hum. Brain Mapp. 29, 802–809 (2008).
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).
Liu, Y. et al. Disrupted small-world networks in schizophrenia. Brain 131, 945–961 (2008).
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).
Lynall, M. E. et al. Functional connectivity and brain networks in schizophrenia. J. Neurosci. 30, 9477–9487 (2010).
Rubinov, M. et al. Small-world properties of nonlinear brain activity in schizophrenia. Hum. Brain Mapp. 30, 403–416 (2009).
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).
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).
Zalesky, A. et al. Disrupted axonal fiber connectivity in schizophrenia. Biol. Psychiatry 69, 80–89 (2011).
Bassett, D. S. et al. Hierarchical organization of human cortical networks in health and schizophrenia. J. Neurosci. 28, 9239–9248 (2008).
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).
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).
Le Gros Clark, W. in Essays on Growth and Form 1–23 (Oxford Univ. Press 1945).
Welker, W. in Cereb Cortex (eds Jones, E. & Peters, A.) 3–136 (Plenum Press, 1990).
Scannell, J. W. Determining cortical landscapes. Nature 386, 452–452 (1997).
Rademacher, J. et al. Probabilistic mapping and volume measurement of human primary auditory cortex. Neuroimage 13, 669–683 (2001).
Hilgetag, C. C. & Barbas, H. Role of mechanical factors in the morphology of the primate cerebral cortex. PLoS Comp. Biol. 2, e22 (2006).
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).
Kirschner, M. & Gerhart, J. Evolvability. Proc. Natl Acad. Sci. USA 95, 8420–8427 (1998).
Newman, M. E. J. Modularity and community structure in networks. Proc. Natl Acad. Sci. USA 103, 8577–8582 (2006).
Lipson, H., Pollack, J. B. & Suh, N. P. On the origin of modular variation. Evolution 56, 1549–1556 (2002).
Kashtan, N. & Alon, U. Spontaneous evolution of modularity and network motifs. Proc. Natl Acad. Sci. USA 102, 13773–13778 (2005).
Variano, E. A., McCoy, J. H. & Lipson, H. Networks, dynamics, and modularity. Phys. Rev. Lett. 92, 188701 (2004).
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).
Zamora-Lopez, G., Zhou, C. S. & Kurths, J. Graph analysis of cortical networks reveals complex anatomical communication substrate. Chaos 19, 015117 (2009).
Zamora-Lopez, G., Zhou, C. & Kurths, J. Exploring brain function from anatomical connectivity. Front. Neurosci. 5, 83 (2011).
Roth, G. & Dicke, U. Evolution of the brain and intelligence. Trends Cogn. Sci. 9, 250–257 (2005).
Changizi, M. A. in The Evolution of Nervous Systems in Mammals (eds Kaas, J. H. & Krubitzer, L.) 181–187 (Academic Press, 2006).
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).
Vaishnavi, S. N. et al. Regional aerobic glycolysis in the human brain. Proc. Natl Acad. Sci. USA 107, 17757–17762 (2010).
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).
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).
The Behavioural and Clinical Neuroscience Institute, University of Cambridge, is supported by the Medical Research Council (UK) and the Wellcome Trust.
Ed Bullmore is a part-time employee and stockholder of GlaxoSmithKline. Olaf Sporns declares no competing financial interests.
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.
Applied to a network, the layout pattern of interconnections, defined in terms of the relations of nodes and edges.
The degree to which the topological properties of a network are resilient to 'lesions' such as the removal of nodes or edges.
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.
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.
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.
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 (N2 − N)/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.
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.
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.
About this article
Cite this article
Bullmore, E., Sporns, O. The economy of brain network organization. Nat Rev Neurosci 13, 336–349 (2012). https://doi.org/10.1038/nrn3214
This article is cited by
Chinese Neurosurgical Journal (2023)
Pathophysiology and probable etiology of cerebral small vessel disease in vascular dementia and Alzheimer’s disease
Molecular Neurodegeneration (2023)
Multiple measurement analysis of resting-state fMRI for ADHD classification in adolescent brain from the ABCD study
Translational Psychiatry (2023)
Nature Communications (2023)
Molecular Psychiatry (2023)