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Open Access 01-05-2016 | Brain Mythology

Is the brain really a small-world network?

Authors: Claus C. Hilgetag, Alexandros Goulas

Published in: Brain Structure and Function | Issue 4/2016

Excerpt

It is commonly assumed that the brain is a small-world network (e.g., Sporns and Honey 2006). Indeed, one of the present authors claimed as much 15 years ago (Hilgetag et al. 2000). The small-worldness is believed to be a crucial aspect of efficient brain organization that confers significant advantages in signal processing (e.g., Lago-Fernández et al. 2000). Correspondingly, the small-world organization is deemed essential for healthy brain function, as alterations of small-world features are observed in patient groups with Alzheimer’s disease (Stam et al. 2007), autism (Barttfeld et al. 2011) or schizophrenia spectrum diseases (Liu et al. 2008; Wang et al. 2012; Zalesky et al. 2011). …

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Amaral L, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci USA 97:11149–11152CrossRefPubMedPubMedCentral

Barttfeld P et al (2011) A big-world network in ASD: dynamical connectivity analysis reflects a deficit in long-range connections and an excess of short-range connections. Neuropsychologia 49:254–263CrossRefPubMed

Bolaños M, Bernat EM, He B, Aviyente S (2013) A weighted small world network measure for assessing functional connectivity. J Neurosci Methods 212:133–142CrossRefPubMed

Braitenberg V, Schüz A (1998) Cortex: statistics and geometry of neuronal connectivity. Springer, BerlinCrossRef

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

Edelman GM, Gally JA (2013) Reentry: a key mechanism for integration of brain function. Front Integr Neurosci 7:63CrossRefPubMedPubMedCentral

Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1–47CrossRefPubMed

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

Garcia GC et al (2012) Building blocks of self-sustained activity in a simple deterministic model of excitable neural networks. Front Comput Neurosci 6:50CrossRefPubMedPubMedCentral

Gómez-Gardeñes J, Zamora-López G, Moreno Y, Arenas A (2010) From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex. PLoS ONE 5:e12313CrossRefPubMedPubMedCentral

Goulas A, Bastiani M, Bezgin G, Uylings HBM, Roebroeck A et al (2014) Comparative analysis of the macroscale structural connectivity in the macaque and human brain. PLoS Comput Biol 10:e1003529CrossRefPubMedPubMedCentral

Herculano-Houzel S (2012) The remarkable, yet not extraordinary, human brain as a scaled-up primate brain and its associated cost. Proc Natl Acad Sci 109:10661–10668CrossRefPubMedPubMedCentral

Hilgetag CC, Hütt M-T (2014) Hierarchical modular brain connectivity is a stretch for criticality. Trends Cogn Sci. doi:10.1016/j.tics.2013.10.016 PubMed

Hilgetag CC, Kaiser M (2004) Clustered organization of cortical connectivity. Neuroinformatics 2:353–360CrossRefPubMed

Hilgetag CC et al (2000) Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. Philos Trans R Soc B 355:91–110CrossRef

Humphries MD, Gurney K (2008) Network “Small-World-Ness”: a quantitative method for determining canonical network equivalence. PLoS ONE 3:e0002051CrossRefPubMed

Humphries MD, Gurney K, Prescott TJ (2006) The brainstem reticular formation is a small-world, not scale-free, network. Proc Biol Sci 273:503–511CrossRefPubMedPubMedCentral

Hütt M-T, Kaiser M, Hilgetag CC (2014) Network-guided pattern formation of neural dynamics. Philos Trans R Soc B 369:20130522CrossRef

Kaiser M, Hilgetag CC (2010) Optimal hierarchical modular topologies for producing limited sustained activation of neural networks. Front Neuroinform 4:8CrossRefPubMedPubMedCentral

Kaiser M et al (2007) Criticality of spreading dynamics in hierarchical cluster networks without inhibition. New J Phys 9:110CrossRef

Klemperer V (1938) Tagebücher 1937–1939, p 122 (“piccolo mondo moderno”), Aufbau Taschenbuch Verlag 1999

Kötter R, Wanke E (2005) Mapping brains without coordinates. Philos Trans R Soc Lond B Biol Sci 360:751–766CrossRefPubMedPubMedCentral

Lago-Fernández LF, Huerta R, Corbacho F, Sigüenza JA (2000) Fast response and temporal coherent oscillations in small-world networks. Phys Rev Lett 84:2758–2761CrossRefPubMed

Li L, Rilling JK, Preuss TM, Glasser MF, Damen FW et al (2012) Quantitative assessment of a framework for creating anatomical brain networks via global tractography. NeuroImage 61:1017–1030CrossRefPubMedPubMedCentral

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

Markov NT et al (2011) Weight consistency specifies regularities of macaque cortical networks. Cereb Cortex 21:1254–1272CrossRefPubMedPubMedCentral

Markov NT et al (2013) Cortical high-density counterstream architectures. Science 342:1238406CrossRefPubMedPubMedCentral

Markov NT et al (2014) A weighted and directed interareal connectivity matrix for macaque cerebral cortex. Cereb Cortex 24:17–36CrossRefPubMedPubMedCentral

Markram H (2006) The blue brain project. Nat Rev Neurosci 7:153–160CrossRefPubMed

Marr C, Hütt M (2006) Similar impact of topological and dynamic noise on complex patterns. Phys Lett A 349:302–305CrossRef

Meunier D, Lambiotte R, Fornito A, Ersche KD, Bullmore ET (2009) Hierarchical modularity in human brain functional networks. Front Neuroinform 3:37. doi:10.3389/neuro.11.037.2009 CrossRefPubMedPubMedCentral

Meunier D, Lambiotte R, Bullmore ET (2010) Modular and hierarchically modular organization of brain networks. Front Neurosci 4:200CrossRefPubMedPubMedCentral

Milgram S (1967) The small world problem. Psychol Today 2:60–67

Modha DS, Singh R (2010) Network architecture of the long-distance pathways in the macaque brain. Proc Natl Acad Sci USA 107:13485–13490CrossRefPubMedPubMedCentral

Moreira A, Mathur A, Diermeier D, Amaral L (2004) Efficient system-wide coordination in noisy environments. Proc Natl Acad Sci USA 101:12085CrossRefPubMedPubMedCentral

Moretti P, Muñoz MA (2013) Griffiths phases and the stretching of criticality in brain networks. Nat Commun 4:2521CrossRefPubMed

Müller-Linow M et al (2008) Organization of excitable dynamics in hierarchical biological networks. PLoS Comput Biol 4:e1000190CrossRefPubMedPubMedCentral

Muñoz MA et al (2010) Griffiths phases on complex networks. Phys Rev Lett 105:128701CrossRefPubMed

Robinson PA et al (2009) Dynamical reconnection and stability constraints on cortical network architecture. Phys Rev Lett 103:108104CrossRefPubMed

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

Rubinov M, Sporns O (2011) Weight-conserving characterization of complex functional brain networks. NeuroImage 56:2068–2079CrossRefPubMed

Samu D, Seth AK, Nowotny T (2014) Influence of wiring cost on the large-scale architecture of human cortical connectivity. PLoS Comput Biol 10:e1003557CrossRefPubMedPubMedCentral

Scannell JW et al (1999) The connectional organization of the cortico-thalamic system of the cat. Cereb Cortex 9:277–299CrossRefPubMed

Shew WL, Plenz D (2013) The functional benefits of criticality in the cortex. Neuroscientist 19:88–100CrossRefPubMed

Sporns O (2006) Small-world connectivity, motif composition, and complexity of fractal neuronal connections. Biosystems 85:55–64CrossRefPubMed

Sporns O, Honey CJ (2006) Small worlds inside big brains. Proc Natl Acad Sci USA 103:19219–19220CrossRefPubMedPubMedCentral

Sporns O et al (2000) Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 10:127–141CrossRefPubMed

Sporns O et al (2004) Organization, development and function of complex brain networks. Trends Cogn Sci 8:418–425CrossRefPubMed

Sporns O et al (2007) Identification and classification of hubs in brain networks. PLoS ONE 10:e1049CrossRef

Stam CJ et al (2007) Small-world networks and functional connectivity in Alzheimer’s disease. Cereb Cortex 17:92–99CrossRefPubMed

Stepanyants A, Martinez LM, Ferecskó AS, Kisvárday ZF (2009) The fractions of short- and long-range connections in the visual cortex. Proc Natl Acad Sci USA 106:3555–3560CrossRefPubMedPubMedCentral

Stephan KE et al (2001) Advanced database methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac). Philos Trans R Soc B 356:1159–1186CrossRef

Telesford QK, Joyce KE, Hayasaka S, Burdette JH, Laurienti PJ (2011) The ubiquity of small-world networks. Brain Connect 1:367–375CrossRefPubMedPubMedCentral

Thomas C, Ye FQ, Okan Irfanoglu M, Modi P, Saleem KS, Leopold DA, Pierpaoli C (2014) Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited. Proc Natl Acad Sci 111:16574–16579CrossRefPubMedPubMedCentral

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

Vanduffel W, Payne BR, Lomber SG, Orban GA (1997) Functional impact of cerebral connections. Proc Natl Acad Sci USA 94:7617–7620CrossRefPubMedPubMedCentral

Wang S-J et al (2011) Sustained activity in hierarchical modular neural networks: self-organized criticality and oscillations. Front Comput Neurosci 5:30PubMedPubMedCentral

Wang Q et al (2012) Anatomical insights into disrupted small-world networks in schizophrenia. NeuroImage 59:1085–1093CrossRefPubMed

Watts DJ, Strogatz SH (1998) Collective dynamics of “small-world” networks. Nature 393:440–442CrossRefPubMed

White JG, Southgate E, Thomson JN, Brenner S (1986) The structure of the nervous system of the nematode Caenorhabditis elegans. Philos Trans R Soc Lond B Biol Sci 314:1–340CrossRefPubMed

Zalesky A, Fornito A (2009) A DTI-derived measure of cortico-cortical connectivity. Trans Med Imaging 28(7):1023–1036CrossRef

Zalesky A, Fornito A, Harding IH, Cocchi L, Yucel M, Pantelis C, Bullmore ET (2010) Whole-brain anatomical networks: does the choice of nodes matter? Neuroimage 50(3):970–983CrossRefPubMed

Zalesky A, Fornito A, Seal ML, Cocchi L, Westin C-F, Bullmore ET, Egan GF, Pantelis C (2011) Disrupted axonal fiber connectivity in schizophrenia. Biol Psychiatry 69:80–89CrossRefPubMed

Zamora-López G et al (2010) Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks. Front Neuroinform 4:1PubMedPubMedCentral

Title: Is the brain really a small-world network?
Authors: Claus C. Hilgetag
Alexandros Goulas
Publication date: 01-05-2016
Publisher: Springer Berlin Heidelberg
Published in: Brain Structure and Function / Issue 4/2016
Print ISSN: 1863-2653
Electronic ISSN: 1863-2661
DOI: https://doi.org/10.1007/s00429-015-1035-6

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