Spatial Complex Brain Network

  • Dong WenEmail author
  • Zhenhao Wei
  • Yanhong Zhou
  • Yanbo Sun
  • Fengnian Li
  • Jiewei Li


This chapter introduces the research status of spatial complex brain networks from the perspective of graph theory and complex networks. Firstly, we review the theoretical concepts of graph theory and complex networks, and combined them with spatial complex brain networks. We focused on a variety of important network topological properties, and then introduced them based on structural connections, functional connections, and cost-effective connections. Three different types of brain networks were established, and further studies on the relationship between structural brain networks and functional brain networks, as well as brain network research based on computational models. Finally, we discussed the future research directions of spatial complex brain networks.


Spatial complex brain Graph theory Complex networks Topological property 


  1. Barabási AL, Albert R. Emergence of scaling in random network. Science. 1999;286(5439):509–12.CrossRefGoogle Scholar
  2. Bassett DS, Meyer-Lindenberg A, Achard S, et al. Adaptive reconfiguration of fractal small world human brain functional networks. Proc Natl Acad Sci U S A. 2006;103(51):19518–23.CrossRefGoogle Scholar
  3. Betzela RF, Bassett DS. Multi-scale brain networks. NeuroImage. 2017;160:73–83.CrossRefGoogle Scholar
  4. Cai SM, Hong L, Wei ZQ, et al. Regression analysis of EEG signals based on complex networks. Journal of University of Science and Technology of China. 2011;41(4):331–7.Google Scholar
  5. Chen J, Liu C, Peng CK. Topological reorganization of EEG functional network is associated with the severity and cognitive impairment in Alzheimer’s disease. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS. 2019;513:588–97.CrossRefGoogle Scholar
  6. Fang X, Jiang Z. Brain functional network analysis based on electroencephalogram. Acta Phys Sin. 2007;56(12):7330–9.Google Scholar
  7. Felleman DJ, Van Essen DC. Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex. 1991;1(1):1–47.CrossRefGoogle Scholar
  8. Fraga González G, Van der Molen MJW, Žarić G, et al. Graph analysis of EEG resting state functional networks in dyslexic readers. Clin Neurophysiol. 2016;127(9):3165–75.CrossRefGoogle Scholar
  9. Li G, Li B, Jiang Y. A new method for automatically modelling brain functional networks. BIOMEDICAL SIGNAL PROCESSING AND CONTROL. 2018;45:70–9.CrossRefGoogle Scholar
  10. Honey CJ, Sporns O, Cammoun L, et al. Predicting human resting-state functional connectivity from structural connectivity. Proc Natl Acad Sci U S A. 2009;106(6):2035–40.CrossRefGoogle Scholar
  11. Honey CJ, Kötter R, Breakspear M, et al. Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc Natl Acad Sci U S A. 2007;104(24):10240–5.CrossRefGoogle Scholar
  12. Hurtado JM, Rubchinsky LL, Sigvardt KA. Statistical method for detection of phase-locking episodes in neural oscillation. J Neurophysiol. 2004;96(4):1883–98.CrossRefGoogle Scholar
  13. White JG, Southgate E, Thomson JN, et al. The structure of the ventral nerve cord of Caenorhabditis elegans. Philos Trans R Soc Lond Ser B Biol Sci. 1976;275(983):327–48.CrossRefGoogle Scholar
  14. Lago-FernÃndez LF, Huerta R, Corbacho F. Fast response and temporal coherent oscillations in small world networks. Phys Rev Lett. 2000;84(12):2758–61.CrossRefGoogle Scholar
  15. Li Y, Liu Y, Li J, et al. Brain anstomical network and intelligence. PLoS Comput Biol. 2009;5(5):e1000395.CrossRefGoogle Scholar
  16. Mesulam M. From sensation to cognition. Brain. 1998;121:1013–52.CrossRefGoogle Scholar
  17. Micheloyannis S, Pachou E, Stam CJ, et al. Small-world networks and disturbed functional connectivity in schizophrenia. Schizophr Res. 2006a;87(123):60–6.CrossRefGoogle Scholar
  18. Micheloyannis S, Pachou E, Stam CJ, et al. Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis. Neurosci Lett. 2006b;402(3):273–7.CrossRefGoogle Scholar
  19. Mohan A, Davidson C, De Ridder D, et al. Effective connectivity analysis of inter- and intramodular hubs in phantom sound perception – identifying the core distress network. Brain Imaging Behav. 2018:1–19.
  20. Murre JM, Sturdy DP. The connectivity of the brain: multi-level quantitative analysis. Biol Cybern. 1995;73(6):529–45.CrossRefGoogle Scholar
  21. Langer N, Pedroni A, Jäncke L. The problem of thresholding in small-world network analysis. PLoS One. 2013;8(1):e53199.CrossRefGoogle Scholar
  22. Pachou E, Vourkas M, Simos P, et al. Working memory in schizophrenia: an EEG study using power apectrum and coherence analysis to estimate cortical activation and network behavior. Brain Topogr. 2008;21(2):128–37.CrossRefGoogle Scholar
  23. Park SM, Kim BJ. Dynamic behaviors in directed networks. Phys Rev E Stat Nonlinear Soft Matter Phys. 2006;74(2 Pt 2):026114.CrossRefGoogle Scholar
  24. Passingham RE, Stephan KE, Kotter R. The anatomical basis of functional localization in cortex. Nat Rev Neurosci. 2002;3(8):606–16.CrossRefGoogle Scholar
  25. Ponten SC, Daffertshofer A, Hillebrand A, et al. The relationship between structural and functional connectivity:graph theoretical analysis of an EEG neural mass model. NeuroImage. 2009;52(3):985–94.CrossRefGoogle Scholar
  26. Rubinov M, Knock SA, Stam CJ, et al. Small-world properties of nonlinear brain activity in schizophrenia. Hum Brain Mapp. 2009;30(2):403–16.CrossRefGoogle Scholar
  27. Schindler KA, Bialonski S, Horstmann MT, et al. Evolving functional network properties and synchronizability during human epileptic seizures. Chaos. 2008;18(3):033119.CrossRefGoogle Scholar
  28. Song S, Sjöström PJ, Reigl M, et al. Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol. 2005;3(3):e68.CrossRefGoogle Scholar
  29. Stam CJ. Functional connectivity patterns of human magnetoencephalographic recordings: a small world network? Neurosci Lett. 2004;355(1/2):25–8.CrossRefGoogle Scholar
  30. Stephan KE, Hilgetag CC, Burns GA. Computational analysis of functional connectivity between areas of primate cerebral cortex. Philos Trans R Soc Lond Ser B Biol Sci. 2000;355(1393):111–26.CrossRefGoogle Scholar
  31. Supekar K, Menon V, Rubin D, et al. Network analysis of intrinsic functional brain connectivity in AD. PLoS Comput Biol. 2008;4(6):e1000100.CrossRefGoogle Scholar
  32. Toppi J, Astolfi L, Risetti M, et al. Different topological properties of EEG-derived networks describe working memory phases as revealed by graph theoretical analysis. Frontiers in Human Neurosience. 2018;11:637.CrossRefGoogle Scholar
  33. Utianski RL, Caviness JN, van Straaten EC, et al. Graph theory network function in Parkinson’s disease assessed with electroencephalography. Clin Neurophysiol. 2016;127(5):2228–36.CrossRefGoogle Scholar
  34. Watts DJ, Strogatz SH. Collective dynamics of small-world networks. Nature. 1998;393(6684):440–2.CrossRefGoogle Scholar
  35. Yin ZL, Li J, Zhang Y. Functional brain network analysis of schizophrenic patients with positive and negative syndrome based on mutual information of EEG time series. BIOMEDICAL SIGNAL PROCESSING AND CONTROL. 2017;31:331–8.CrossRefGoogle Scholar
  36. Zhu G, Wang C, Liu F, et al. Age-related network topological difference based on the sleep ECG signal. Physiol Meas. 2018;39(8):084009.CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Dong Wen
    • 1
    Email author
  • Zhenhao Wei
    • 1
  • Yanhong Zhou
    • 2
  • Yanbo Sun
    • 1
  • Fengnian Li
    • 3
  • Jiewei Li
    • 4
  1. 1.School of Information Science and EngineeringYanshan UniversityQinhuangdaoChina
  2. 2.School of Mathematics and Information Science and TechnologyHebei Normal University of Science and TechnologyQinhuangdaoChina
  3. 3.Yanshan University LibraryYanshan UniversityQinhuangdaoChina
  4. 4.Department of Electrical and Electronic EngineeringThe University of Hong KongHong KongChina

Personalised recommendations