Small-world brain networks

Neuroscientist

Volumn 12, Issue 6, 2006, Pages 512-523

  Bassett, Danielle Smith ^a,b,c   Bullmore, Ed ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c NATIONAL INSTITUTE OF MENTAL HEALTH   (United States)

Author keywords

Functional magnetic resonance imaging; Graph theory; Human brain functional networks; Small world network

Indexed keywords

BRAIN FUNCTION; ELECTROENCEPHALOGRAM; FUNCTIONAL MAGNETIC RESONANCE IMAGING; HUMAN; INFORMATION PROCESSING; MAGNETOENCEPHALOGRAPHY; MATHEMATICAL MODEL; NONHUMAN; PRIORITY JOURNAL; REVIEW;

ANIMALS; BRAIN; BRAIN MAPPING; HUMANS; MODELS, NEUROLOGICAL; NERVE NET;

EID: 33750466904     PISSN: 10738584     EISSN: 10894098     Source Type: Journal    
DOI: 10.1177/1073858406293182     Document Type: Review

References (69)

1. Achard S, Salvador R, Whitcher B, Suckling J, Bullmore E. 2006. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J Neurosci 26:63-72.
2. Albert R, Barabási A-L. 2000. Topology of evolving networks: local events and universality. Phys Rev Lett 85:5234-7.
3. Albert R, Barabási A-L. 2002. Statistical mechanics of complex networks. Rev Mod Phys 74(1):47.
4. Allman JM. 1998. Evolving brains. New York: Scientific American.
5. Amaral LAN, Scala A, Barthelemy M, Stanley HE. 2000. Classes of small-world networks. Proc Natl Acad Sci U S A 97:11149-52.
6. Atay FM, Biyikoglu T. 2005. Graph operations and synchronization of complex networks. Phys Rev E 72:016217.
7. Atay FM, Biyikoglu T, Jost J. 2006. Synchronization of networks with prescribed degree distributions. IEEE Transactions on Circuits and Systems Part I: Regular Papers 53(1):92-8.
8. Barahona M, Pecora LM. 2002. Synchronization in small-world systems. Phys Rev Lett 89:054101.
9. Bianconi G, Barabási A-L. 2001. Competition and multiscaling in evolving networks. Europhys Lett 54:436.
10. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU. 2006. Complex networks: structure and dynamics. Phys Rep 424:175-308.
11. Buchanan M. 2003. Small world: uncovering nature's hidden networks: London: Orion.
12. Buzsáki G, Geisler C, Henze DA, Wang X-J. 2004. Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci 27:186-93.
13. Changizi MA. 2001. Principles underlying mammalian neocortical scaling. Biol Cybern 84:207-15.
14. Chklovskii DB. 2004. Synaptic connectivity and neuronal morphology: two sides of the same coin. Neuron 43:609-17.
15. Chklovskii DB, Schikorski T, Stevens CF. 2002. Wiring optimization in cortical circuits. Neuron 34:341-7.
16. Costa LdF, Rodrigues FA, Travieso G, Boas PRV. 2006. Characterization of complex networks: a survey of measurements. Available from: http://arxiv.org/ abs/cond-mat/0505185.
17. Costa LdF, Sporns O. 2005. Hierarchical features of large-scale cortical connectivity. Eur Phys JB 48:567-73.
18. Dorogovtsev SN, Mendes JFF. 2000. Evolution of networks with aging of sites. Phys Rev E 62:1842.
19. Dorogovtsev SN, Mendes JFF, Samukhin AN. 2000. Structure of growing networks with preferential linking. Phys Rev Lett 85:4633.
20. Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV. 2005. Scale-free brain functional networks. Phys Rev Lett 94:018102.
21. Felleman DJ, Van Essen DC. 1991. Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1-47.
22. Friston KJ. 1994. Functional and effective connectivity in neuroimaging: a synthesis. Hum Brain Mapp 2:56-78.
23. Gao Z, Hu B, Hu G. 2001. Stochastic resonance of small-world networks. Phys Rev E 65:016209.
24. Hilgetag CC, Burns GAPC, O'Neill MA, Scannell JW. 2000. Anatomical connectivity defines the organization of clusters of cortical areas in the macaque and the cat. Philos Trans R Soc Lond B Biol Sci 355:91.
25. Hilgetag CC, Grant S. 2000. Uniformity, specificity and variability of corticocortical connectivity. Philos Trans R Soc Lond B Biol Sci 355:7-20.
26. Hong H, Choi MY. 2002. Synchronization on small-world networks. Phys Rev E 65:026139.
27. Humphries M, Gurney K, Prescott T. 2006. The brainstem reticular formation is a small-world, not scale-free, network. Philos Trans R Soc Lond B Biol Sci 273:503-11.
28. Jeong H, Neda Z, Barabási A-L. 2003. Measuring preferential attachment for evolving networks. Europhys Lett 61:567-72.
29. Kaiser M, Hilgetag CC. 2004a. Spatial growth of real-world networks. Phys Rev E 69:036103.
30. Kaiser M, Hilgetag CC. 2004b. Modelling the development of cortical systems networks. Neurocomputing 2004:297-302.
31. Karbowski J. 2001. Optimal wiring principle and plateaus in the degree of separation for cortical neurons. Phys Rev Lett 86:3674.
32. Koch C, Laurent G. 1999. Complexity and the nervous system. Science 284:96-8.
33. Kötter R, Sommer FT. 2000. Global relationship between structural connectivity propagation in the cerebral cortex. Philos Trans R Soc Lond B Biol Sci 355:127-34.
34. Krapivsky PL, Redner S, Leyvraz F. 2000. Connectivity of growing random networks. Phys Rev Lett 85:4629.
35. Lago-Fernandez LF, Huerta R, Corbacho F, Siguenza JA. 2000. Fast response and temporal coherent oscillations in small-world networks. Phys Rev Lett 84:2758-61.
36. Latora V, Marchiori M. 2001. Efficient behavior of small-world networks. Phys Rev Lett 87:198701.
37. Latora V, Marchiori M. 2003. Economic small-world behavior in weighted networks. Euro Phys JB 32:249-63.
38. Lu J, Yu K, Chen G, Cheng D. 2004. Characterizing the synchronizability of small-world dynamical networks. IEEE Transactions on Circuits and Systems Part I: Regular Papers 51:787-96.
39. Masuda N, Aihara K. 2004. Global and local synchrony of coupled neurons in small-world networks. Biol Cybern 90:302-9.
40. Micheloyannis S, Pachou E, Stam CJ, Vourkas M, Erimaki S, Tsirka V. 2006. Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis. Neurosci Lett 402:273-7.
41. Newman MEJ, Watts DJ. 1999. Scaling and percolation in the small-world network model. Phys Rev E 60:7332.
42. Nishikawa T, Motter AE, Lai Y-C, Hoppensteadt FC. 2003. Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? Phys Rev Lett 91:014101.
43. Ozik J, Hunt BR, Ott E. 2004. Growing networks with geographical attachment preference: emergence of small worlds. Phys Rev E 69:026108.
44. Percha B, Dzakpasu R, Zochowski M, Parent J. 2005. Transition from local to global phase synchrony in small world neural network and its possible implications for epilepsy. Phys Rev E 72:031909.
45. Ringo JL. 1991. Neuronal interconnection as a function of brain size. Brain Behav Evol 38:1-6.
46. Salvador R, Suckling J, Coleman MR, Pickard JD, Menon D, Bullmore E. 2005. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb Cortex 15:1332-42.
47. Salvador R, Suckling J, Schwarzbauer C, Bullmore E. 2005. Undirected graphs of frequency-dependent functional connectivity in whole brain networks. Philos Trans R Soc Lond B Biol Sci 360:937.
48. Scannell JW, Blakemore C, Young MP. 1995. Analysis of connectivity in the cat cerebral cortex. J Neurosci 15:1463-83.
49. Scannell JW, Burns GAPC, Hilgetag CC, O'Neil MA, Young MP. 1999. The connectional organization of the cortico-thalamic system of the cat. Cereb Cortex 9:277-99.
50. Schank T, Wagner D. 2005. Approximating clustering coefficient and transitivity. Journal of Graph Algorithms and Applications 9:265-75.
51. Sik A, Penttonen M, Ylinen A, Buzsáki G. 1995. Hippocampal CA1 interneurons: an in vivo intracellular labeling study. J Neurosci 15:6651-65.
52. Simard D, Nadeau L, Kroger H. 2005. Fastest learning in small-world neural networks. Phys Lett A 336:8-15.
53. Sporns O, Chialvo DR, Kaiser M, Hilgetag CC. 2004. Organization, development and function of complex brain networks. Trends Cogn Sci 8:418-25.
54. Sporns O, Tononi G, Edelman GM. 2000. Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 10:127-41.
55. Sporns O, Tononi G, Edelman GM. 2002. Theoretical neuroanatomy and the connectivity of the cerebral cortex. Behav Brain Res 135:69-744.
56. Sporns O, Zwi J. 2004. The small world of the cerebral cortex. Neuroinformatics 2:145-62.
57. Stam CJ. 2004. Functional connectivity patterns of human magnetoencephalographic recordings: a "small-world" network? Neurosci Lett 355:25-8.
58. Stam CJ, Jones BF, Nolle G, Breakspear M, Scheltens P. 2006. Small-world networks and functional connectivity in Alzheimer's disease. Cereb Cortex. Epub ahead of print February 1, 2006.
59. Stepanyants A, Hof PR, Chklovskii DB. 2002. Geometry and structural plasticity of synaptic connectivity. Neuron 34:275-88.
60. Stephan K, Hilgetag CC, Burns GAPC, O'Neill MA, Young MP, Kötter R. 2000. Computational analysis of functional connectivity between areas of primate cerebral cortex. Philos Trans R Soc Lond B Biol Sci 355:111-26.
61. Vragovic I, Louis E, Diaz-Guilera A. 2005. Efficiency of informational transfer in regular and complex networks. Phys Rev E 71:036122.
62. Watts DJ. 2004a. Six degrees: the new science of networks. New York: Vintage.
63. Watts DJ. 2004b. Small worlds: the dynamics of networks between order and randomness. Princeton (NJ): Princeton University Press.
64. Watts DJ, Strogatz SH. 1998. Collective dynamics of "small- world" networks. Nature 393:440-2.
65. Xulvi-Brunet R, Sokolov IM. 2002. Evolving networks with disadvantaged long-range connections. Phys Rev E 66:026118.
66. Young MP. 1992. Objective analysis of the topological organization of the primate cortical visual system. Nature 358:152-5.
67. Young MP. 1993. The organization of neural systems in the primate cerebral cortex. Proc R Soc Lond B 252:13-8.
68. Young MP, Scannell JW, O'Neill MA, Hilgetag CC, Burns GAPC, Blakemore C. 1995. Non-metric multidimensional scaling in the analysis of neuroanatomical connection data and the organization of the primate cortical visual system. Philos Trans R Soc Lond B Biol Sci 348:281-308.
69. Zhigulin VP. 2005. Dynamical motifs: building blocks of complex dynamics in sparsely connected random networks. Phys Rev Lett 92:238701.