Generative models of rich clubs in Hebbian neuronal networks and large-scale human brain networks
Open accessAbstract
Rich clubs arise when nodes that are ‘rich’ in connections also form an elite, densely connected ‘club’. In brain networks, rich clubs incur high physical connection costs but also appear to be especially valuable to brain function. However, little is known about the selection pressures that drive their formation. Here, we take two complementary approaches to this question: firstly we show, using generative modelling, that the emergence of rich clubs in large-scale human brain networks can be driven by an economic trade-off between connection costs and a second, competing topological term. Secondly we show, using simulated neural networks, that Hebbian learning rules also drive the emergence of rich clubs at the microscopic level, and that the prominence of these features increases with learning time. These results suggest that Hebbian learning may provide a neuronal mechanism for the selection of complex features such as rich clubs. The neural networks that we investigate are explicitly Hebbian, and we argue that the topological term in our model of large-scale brain connectivity may represent an analogous connection rule. This putative link between learning and rich clubs is also consistent with predictions that integrative aspects of brain network organization are especially important for adaptive behaviour.
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Network models of development appear complementary to traditional models such as Hebbian learning.
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Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060 · see citing works
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135 · see citing works
Community structure in social and biological networks
Girvan, M., & Newman, M. E. J. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.122653799 · Cited by 15,502 · see citing works
Complex brain networks: graph theoretical analysis of structural and functional systems
Bullmore, E., & Sporns, O. (2009) · Nature Reviews Neuroscience · doi:10.1038/nrn2575 · Cited by 11,820 · see citing works
Self-citationComplex network measures of brain connectivity: Uses and interpretations
Rubinov, M., & Sporns, O. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2009.10.003 · Cited by 11,522 · see citing works
A set of measures of centrality based upon betweenness
Freeman, L. (1977) · Sociometry · doi:10.2307/3033543 · Cited by 10,557 · see citing works
Error and attack tolerance of complex networks
Albert, R., Jeong, H., & Barabási, A.-L. (2000) · Nature · doi:10.1038/35019019 · Cited by 7,534 · see citing works
Error and attack tolerance of complex networksPreprint
Albert, R., Jeong, H., & Barabási, A.-Ĺ. (2000) · Cited by 6,554 · see citing works
The Architecture of Complexity
Simon, H. (1991) · Springer eBooks · doi:10.1007/978-1-4899-0718-9_31 · Cited by 6,459 · see citing works
The structure of the nervous system of the nematode <i>Caenorhabditis elegans</i>
White, J. G., Southgate, E., Thomson, J. N., & Brenner, S. (1986) · Philosophical Transactions of the Royal Society of London. B, Biological Sciences · doi:10.1098/rstb.1986.0056 · Cited by 5,589 · see citing works
Milgram, S. (1967) · PsycEXTRA Dataset · doi:10.1037/e400002009-005 · Cited by 5,528 · see citing works
Fast algorithm for detecting community structure in networks
Newman, M. E. J. (2004) · Physical Review E · doi:10.1103/physreve.69.066133 · Cited by 5,415 · see citing works
Efficient behavior of small-world networks
Latora, V., & Marchiori, M. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.198701 · Cited by 5,119 · see citing works
Simple model of spiking neurons
Izhikevich, E. M. (2003) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2003.820440 · Cited by 4,828 · see citing works
The economy of brain network organization
Bullmore, E., & Sporns, O. (2012) · Nature Reviews Neuroscience · doi:10.1038/nrn3214 · Cited by 3,284 · see citing works
Self-citationPrice, D. J. D. S. (1965) · Science · doi:10.1126/science.149.3683.510 · Cited by 3,121 · see citing works
Competitive Hebbian learning through spike-timing-dependent synaptic plasticity
Song, S., Miller, K. D., & Abbott, L. F. (2000) · Nature Neuroscience · doi:10.1038/78829 · Cited by 2,738 · see citing works
Rich-club organization of the human connectome
van den Heuvel, M. P., & Sporns, O. (2011) · The Journal of Neuroscience · doi:10.1523/jneurosci.3539-11.2011 · Cited by 2,354 · see citing works
Spike Timing–Dependent Plasticity: A Hebbian Learning Rule
Caporale, N., & Dan, Y. (2008) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.31.060407.125639 · Cited by 1,997 · see citing works
Attack vulnerability of complex networks
Holme, P., Kim, B. J., Yoon, C. N., & Han, S. K. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.056109 · Cited by 1,902 · see citing works
Community Structure in Directed Networks
Leicht, E. A., & Newman, M. E. J. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.118703 · Cited by 1,118 · see citing works
Polychronization: Computation with Spikes
Izhikevich, E. M. (2005) · Neural Computation · doi:10.1162/089976606775093882 · Cited by 1,066 · see citing works
Energy limitation as a selective pressure on the evolution of sensory systems
Niven, J. E., & Laughlin, S. B. (2008) · Journal of Experimental Biology · doi:10.1242/jeb.017574 · Cited by 1,056 · see citing works
Detecting rich-club ordering in complex networks
Colizza, V., Flammini, A., Serrano, M. A., & Vespignani, A. (2006) · Nature Physics · doi:10.1038/nphys209 · Cited by 1,001 · see citing works
The Architecture of Complexity
Barabási, A.-Ĺ. (2007) · IEEE Control Systems · doi:10.1109/mcs.2007.384127 · Cited by 819 · see citing works
Development of large-scale functional brain networks in children
Supekar, K., Musen, M., & Menon, V. (2009) · PLoS Biology · doi:10.1371/journal.pbio.1000157 · Cited by 807 · see citing works
Analyzing and modeling real-world phenomena with complex networks: a survey of applications
Costa, L. D. F., Oliveira, O. N., Travieso, G., Rodrigues, F. A., Villas-Boas, P. R., Antiqueira, L., Viana, M. P., & Rocha, L. E. C. (2011) · Advances In Physics · doi:10.1080/00018732.2011.572452 · Cited by 804 · see citing works
High-cost, high-capacity backbone for global brain communication
van den Heuvel, M. P., Kahn, R. S., Goñi, J., & Sporns, O. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1203593109 · Cited by 781 · see citing works
Cartography of complex networks: modules and universal roles
Guimerà, R., & Amaral, L. A. N. (2005) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2005/02/p02001 · Cited by 757 · see citing works
Modeling the Internet's large-scale topology
Yook, S., Jeong, H., & Barabási, A.-Ĺ. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.172501399 · Cited by 667 · see citing works
Braitenberg, V., & Schüz, A. (1991) · Studies of brain function · doi:10.1007/978-3-662-02728-8 · Cited by 659 · see citing works
Wiring optimization can relate neuronal structure and function
Chen, B. L., Hall, D. H., & Chklovskii, D. B. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0506806103 · Cited by 650 · see citing works
Abnormal Rich Club Organization and Functional Brain Dynamics in Schizophrenia
van den Heuvel, M. P., Sporns, O., Collin, G., Scheewe, T. W., Mandl, R. C. W., Cahn, W., Goñi, J., Pol, H. E. H., & Kahn, R. S. (2013) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2013.1328 · Cited by 646 · see citing works
Popularity versus similarity in growing networks
Papadopoulos, F., Kitsak, M., Serrano, M. Á., Boguñá, M., & Krioukov, D. (2012) · Nature · doi:10.1038/nature11459 · Cited by 634 · see citing works
The Rich-Club Phenomenon in the Internet Topology
Zhou, S., & Mondragón, R. J. (2004) · IEEE Communications Letters · doi:10.1109/lcomm.2004.823426 · Cited by 618 · see citing works
Exuberance in the development of cortical networks
Innocenti, G. M., & Price, D. J. (2005) · Nature Reviews Neuroscience · doi:10.1038/nrn1790 · Cited by 512 · see citing works
Cognitive relevance of the community structure of the human brain functional coactivation network
Crossley, N. A., Mechelli, A., Vértes, P. E., Winton‐Brown, T., Patel, A. X., Ginestet, C. E., McGuire, P. K., & Bullmore, E. T. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1220826110 · Cited by 449 · see citing works
Self-citationAn anatomical substrate for integration among functional networks in human cortex
van den Heuvel, M. P., & Sporns, O. (2013) · The Journal of Neuroscience · doi:10.1523/jneurosci.2128-13.2013 · Cited by 404 · see citing works
Simple models of human brain functional networks
Vértes, P. E., Alexander‐Bloch, A. F., Gogtay, N., Giedd, J. N., Rapoport, J. L., & Bullmore, E. T. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1111738109 · Cited by 359 · see citing works
Self-citationThe Rich Club of the<i>C. elegans</i>Neuronal Connectome
Towlson, E. K., Vértes, P. E., Ahnert, S. E., Schafer, W. R., & Bullmore, E. T. (2013) · The Journal of Neuroscience · doi:10.1523/jneurosci.3784-12.2013 · Cited by 343 · see citing works
Self-citationDevelopmental Changes in Organization of Structural Brain Networks
Khundrakpam, B. S., Reid, A., Brauer, J., Carbonell, F., Lewis, J., Ameis, S., Karama, S., Lee, J., Chen, Z., Das, S., et al. (2013) · Cerebral Cortex · doi:10.1093/cercor/bhs187 · Cited by 234 · see citing works
Spatial growth of real-world networks
Kaiser, M., & Hilgetag, C. C. (2004) · Physical Review E · doi:10.1103/physreve.69.036103 · Cited by 201 · see citing works
Rich Club Organization and Intermodule Communication in the Cat Connectome
de Reus, M. A., & van den Heuvel, M. P. (2013) · Journal of Neuroscience · doi:10.1523/jneurosci.1448-13.2013 · Cited by 164 · see citing works
Modelling the development of cortical systems networks
Kaiser, M., & Hilgetag, C. C. (2004) · Neurocomputing · doi:10.1016/j.neucom.2004.01.059 · Cited by 153 · see citing works
Phase transition in the economically modeled growth of a cellular nervous system
Nicosia, V., Vértes, P. E., Schafer, W. R., Latora, V., & Bullmore, E. T. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1300753110 · Cited by 83 · see citing works
Self-citationEffect of network topology on neuronal encoding based on spatiotemporal patterns of spikes
Vértes, P. E., & Duke, T. A. J. (2010) · HFSP journal · doi:10.2976/1.3386761 · Cited by 22 · see citing works
Self-citationParticle content of the nonlinear sigma model with a θ-term: a lattice model investigation
Venuti, L. C., Boschi, C. D. E., Ercolessi, E., Ortolani, F., Morandi, G., Pasini, S., & Roncaglia, M. (2005) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2005/02/l02004 · Cited by 19 · see citing works
Computation in spiking neural networks
Koh, L. (2012) · DR-NTU (Nanyang Technological University) · Cited by 2 · see citing works
Flagged first, then by citations
2 of the 50 references couldn’t be matched to a known paper.
Cited by
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Small-World Brain Networks Revisited
Bassett, D. S., & Bullmore, E. T. (2016) · The Neuroscientist · doi:10.1177/1073858416667720 · Cited by 847 · see citing works
Self-citationVértes, P. E., Rittman, T., Whitaker, K. J., Romero-García, R., Váša, F., Kitzbichler, M. G., Wagstyl, K., Fonagy, P., Dolan, R. J., Jones, P. B., et al. (2016) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2015.0362 · Cited by 200 · see citing works
Self-citationCombining complex networks and data mining: Why and how
Zanin, M., Papo, D., Sousa, P. A., Menasalvas, E., Nicchi, A., Kubik, E., & Boccaletti, S. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.04.005 · Cited by 185 · see citing works
Complex network theory and the brain
Papo, D., Buldú, J. M., Boccaletti, S., & Bullmore, E. T. (2014) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2013.0520 · Cited by 155 · see citing works
Self-citationGenerative models for network neuroscience: prospects and promise
Betzel, R. F., & Bassett, D. S. (2017) · Journal of The Royal Society Interface · doi:10.1098/rsif.2017.0623 · Cited by 127 · see citing works
Micro-connectomics: probing the organization of neuronal networks at the cellular scale
Schröter, M. S., Paulsen, O., & Bullmore, E. T. (2017) · Nature reviews. Neuroscience · doi:10.1038/nrn.2016.182 · Cited by 123 · see citing works
Self-citationShared vulnerability for connectome alterations across psychiatric and neurological brain disorders
de Lange, S. C., Scholtens, L. H., Initiative, A. D. N., van den Berg, L. H., Boks, M. P., Bozzali, M., Cahn, W., Dannlowski, U., Durston, S., Geuze, E., et al. (2019) · Nature Human Behaviour · doi:10.1038/s41562-019-0659-6 · Cited by 120 · see citing works
Network topology and functional connectivity disturbances precede the onset of Huntington’s disease
Harrington, D. L., Rubinov, M., Durgerian, S., Mourany, L., Reece, C., Koenig, K. A., Bullmore, E. T., Long, J. D., Paulsen, J. S., for the PREDICT-HD investigators of the Huntington Study Group, et al. (2015) · Brain · doi:10.1093/brain/awv145 · Cited by 121 · see citing works
Self-citationBassett, D. S., & Mattar, M. G. (2017) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2017.01.010 · Cited by 106 · see citing works
Rich-club neurocircuitry: function, evolution, and vulnerability
Griffa, A., & van den Heuvel, M. P. (2018) · Dialogues in Clinical Neuroscience · doi:10.31887/dcns.2018.20.2/agriffa · Cited by 94 · see citing works
Human brain development over the early years
Haartsen, R., Jones, E. J. H., & Johnson, M. H. (2016) · Current Opinion in Behavioral Sciences · doi:10.1016/j.cobeha.2016.05.015 · Cited by 82 · see citing works
Structural MRI of brain similarity networks
Sebenius, I., Dorfschmidt, L., Seidlitz, J., Alexander‐Bloch, A. F., Morgan, S. E., & Bullmore, E. T. (2024) · Nature reviews. Neuroscience · doi:10.1038/s41583-024-00882-2 · Cited by 81 · see citing works
Self-citationHart, M. G., Ypma, R. J. F., Romero-Garcia, R., Price, S. J., & Suckling, J. (2016) · Journal of Neurosurgery · doi:10.3171/2015.4.jns142683 · Cited by 74 · see citing works
Opportunities and Challenges for Psychiatry in the Connectomic Era
Fornito, A., Bullmore, E. T., & Zalesky, A. (2017) · Biological Psychiatry: Cognitive Neuroscience and Neuroimaging · doi:10.1016/j.bpsc.2016.08.003 · Cited by 74 · see citing works
Self-citationOldham, S., Fulcher, B., Aquino, K. M., Arnatkevičiūtė, A., Paquola, C., Shishegar, R., & Fornito, A. (2022) · Science Advances · doi:10.1126/sciadv.abm6127 · Cited by 59 · see citing works
Emerging Frontiers of Neuroengineering: A Network Science of Brain Connectivity
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Colloquium: Multiscale modeling of brain network organization
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Efficient coding in the economics of human brain connectomics
Zhou, D., Lynn, C. W., Cui, Z., Ćirić, R., Baum, G. L., Moore, T. M., Roalf, D. R., Detre, J. A., Gur, R. C., Gur, R. E., et al. (2021) · Network Neuroscience · doi:10.1162/netn_a_00223 · Cited by 38 · see citing works
Wang, S., Li, Y., Qiu, S., Zhang, C., Wang, G., Xian, J., Li, T., & He, H. (2020) · NeuroImage Clinical · doi:10.1016/j.nicl.2020.102188 · Cited by 32 · see citing works
Homophilic wiring principles underpin neuronal network topology in vitro
Akarca, D., Dunn, A. W., Hornauer, P., Ronchi, S., Michele, F., Wang, C., Terrigno, M., Jagasia, R., Vértes, P. E., Mierau, S. B., et al. (2025) · eLife · doi:10.7554/elife.85300 · Cited by 29 · see citing works
Self-citationToward computational neuroconstructivism: a framework for developmental systems neuroscience
Astle, D. E., Johnson, M. H., & Akarca, D. (2023) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2023.04.009 · Cited by 29 · see citing works
Nonlinear growth: an origin of hub organization in complex networks
Bauer, R., & Kaiser, M. (2017) · Royal Society Open Science · doi:10.1098/rsos.160691 · Cited by 23 · see citing works
Network topology of the marmoset connectome
Liu, Z.-Q., Zheng, Y., & Mišić, B. (2020) · Network Neuroscience · doi:10.1162/netn_a_00159 · Cited by 19 · see citing works
Simpson, S., Chen, Y., Wellmeyer, E., Smith, L. C., Montes, B. A., George, O., & Kimbrough, A. (2021) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2021.595507 · Cited by 16 · see citing works
Gabrieli, D. J., Schumm, S. N., Vigilante, N. F., & Meaney, D. F. (2020) · Neural Computation · doi:10.1162/neco_a_01343 · Cited by 15 · see citing works
Synaptic Plasticity and Spike Synchronisation in Neuronal Networks
Borges, R. R., Borges, F. S., Lameu, E. L., Protachevicz, P. R., Iarosz, K. C., Caldas, I. L., Viana, R. L., Macau, E. E. N., Baptista, M. S., Grebogi, C., et al. (2017) · Brazilian Journal of Physics · doi:10.1007/s13538-017-0529-5 · Cited by 13 · see citing works
From calcium imaging to graph topology
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Combining complex networks and data mining: why and howPreprint
Zanin, M., Papo, D., Sousa, P., Menasalvas, E., Nicchi, A., Kubik, E., & Boccaletti, S. (2016) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/054064 · Cited by 13 · see citing works
Abnormal white‐matter rich‐club organization in obsessive–compulsive disorder
Baldi, S., Michielse, S., Vriend, C., van den Heuvel, M. P., van den Heuvel, O. A., Schruers, K. R. J., & Goossens, L. (2022) · Human Brain Mapping · doi:10.1002/hbm.25984 · Cited by 11 · see citing works
Small-World Brain Networks RevisitedPreprint
Bassett, D. S., & Bullmore, E. T. (2016) · arXiv (Cornell University) · doi:10.17863/cam.4889 · Cited by 13 · see citing works
Self-citationEarly adversity changes the economic conditions of structural brain network organisationPreprint
Carozza, S., Holmes, J., Vértes, P. E., Bullmore, E. T., Arefin, T. M., Pugliese, A., Zhang, J., Kaffman, A., Akarca, D., & Astle, D. E. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.06.08.495303 · Cited by 10 · see citing works
Self-citationGrowing Homophilic Networks Are Natural Navigable Small Worlds
Malkov, Y. A., & Ponomarenko, A. (2016) · PLoS ONE · doi:10.1371/journal.pone.0158162 · Cited by 9 · see citing works
The missing link: Predicting connectomes from noisy and partially observed tract tracing data
Hinne, M., Meijers, A., Bakker, R., Tiesinga, P. H. E., Mørup, M., & van Gerven, M. A. J. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005374 · Cited by 9 · see citing works
The growing topology of the C. elegans connectomePreprint
Helm, A., Blevins, A. S., & Bassett, D. S. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2101.00065 · Cited by 9 · see citing works
Early adversity changes the economic conditions of mouse structural brain network organization
Carozza, S., Holmes, J., Vértes, P. E., Bullmore, E. T., Arefin, T. M., Pugliese, A., Zhang, J., Kaffman, A., Akarca, D., & Astle, D. E. (2023) · Developmental Psychobiology · doi:10.1002/dev.22405 · Cited by 7 · see citing works
Self-citationFrom phenotype to genotype in complex brain networks
Zanin, M., Correia, M., Sousa, P., & Cruz, J. (2016) · Scientific Reports · doi:10.1038/srep19790 · Cited by 6 · see citing works
Carozza, S., Holmes, J., Akarca, D., & Astle, D. E. (2024) · Developmental Science · doi:10.1111/desc.13490 · Cited by 4 · see citing works
Qian, Y., & Zhang, Z. (2016) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2016.11.012 · Cited by 5 · see citing works
Geometric constraints on the architecture of mammalian cortical connectomes
Normand, F., Gajwani, M., Cao, T. N., Cruddas, J., Sangchooli, A., Oldham, S., Holmes, A., Robinson, P. A., Pang, J. C. S., & Fornito, A. (2026) · Cell · doi:10.1016/j.cell.2026.05.048 · Cited by 4 · see citing works
Probabilistic Constraint Programming for Parameters Optimisation of Generative Models
Zanin, M., Correia, M., Sousa, P., & Cruz, J. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-23485-4_38 · Cited by 2 · see citing works
Uncertainty in Functional Network Representations of Brain Activity of Alcoholic Patients
Zanin, M., Belkoura, S., Gómez, J., Álfaro, C., & Cano, J. (2020) · Brain Topography · doi:10.1007/s10548-020-00799-w · Cited by 2 · see citing works
Emerging Frontiers of Neuroengineering: A Network Science of Brain ConnectivityPreprint
Bassett, D. S., Khambhati, A. N., & Grafton, S. T. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1612.08059 · Cited by 2 · see citing works
Multiscale modeling of brain network organizationPreprint
Presigny, C., & Fallani, F. D. V. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.13473 · Cited by 2 · see citing works
Schizophrenia in the Era of Brain Complexity
Collin, G., & Kahn, R. S. (2016) · The Journal of Nervous and Mental Disease · doi:10.1097/nmd.0000000000000545 · Cited by 1 · see citing works
Network Models in Neuroscience
Bassett, D. S., Zurn, P., & Gold, J. I. (2019) · The MIT Press eBooks · doi:10.7551/mitpress/12593.003.0011 · Cited by 1 · see citing works
Growing homophilic networks are natural optimally wired navigable small worldsPreprint
Malkov, Y. A. (2015) · arXiv (Cornell University) · Cited by 1 · see citing works
Novel Gain of Function Mouse Model of KCNT1-Related EpilepsyPreprint
Olguin, S. L., Davis, D., Rehman, A., Berg, S. W., Sahagún, E., Oswalt, P. S., Patil, M., Sullivan, P. D. M., Zhang, B., Bryda, E. C., et al. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.07.22.666003 · Cited by 1 · see citing works
Growing homophilic networks are natural optimal navigable small worldsPreprint
Malkov, Y. A. (2015) · arXiv (Cornell University) · doi:10.13140/rg.2.1.3046.1283
Baldi, S. (2023) · doi:10.26481/dis.20230526sb
Ritchison, G. (2023) · Fascinating life sciences · doi:10.1007/978-3-031-14852-1_4
- Authors
- Vértes, P. E., Alexander-Bloch, A., & Bullmore, E. T.
- Affiliations
- University of Cambridge (GB)
- Behavioural and Clinical Neuroscience Institute, Department of Psychiatry, University of Cambridge, Cambridge, UK
- GlaxoSmithKline (United Kingdom) (GB)
- Corresponding author
- Vértes, Petra E.
- Venue
- Philosophical Transactions of the Royal Society B: Biological Sciences
- Publisher
- The Royal Society
- Published
- 2014-10-05
- Volume
- 369
- Issue
- 1653
- Pages
- 20130531
- ISSN
- 0962-8436 (ISSN-L)
- 1471-2970
- PMC
- PMC4150306
- OpenAlex
- W1988516611
- Cited by
- 50
- References
- 50
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 2 · 2023: 4 · 2022: 5 · 2021: 3 · 2020: 5 · 2019: 2 · 2018: 1 · 2017: 7 · 2016: 12 · 2015: 5 · 2014: 1
- FWCI
- 4.65
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Philosophical Transactions of the Royal Society B Biological Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Wellcome Trust (095844/Z/11/Z, 095844, 093875)
- National Institute for Health and Care Research (NF-SI-0513-10051)
- Medical Research Council (MR/K020706/1)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Keywords
- rich club, Hebbian learning, brain connectivity, large-scale brain networks, generative network models, connection cost, network topology, neural network simulation
- MeSH terms
- Brain, Computer Simulation, Humans, Models, Neurological, Nerve Net, Organogenesis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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