Dynamics of Hierarchical Neural Networks

  • Claus C. HilgetagEmail author
  • Mark Müller-Linow
  • Marc-Thorsten Hütt
Conference paper


Neural networks are organized hierarchically across many scales of dimension, from cellular neuronal circuits via mesoscopic networks at the level of columns, layers and areas to large-scale brain systems. However, the structural organization and dynamic capabilities of hierarchical networks are still poorly characterized. We investigated the contribution of different features of network topology to the dynamic behavior of hierarchically organized neural networks. Prototypical representatives of different types of hierarchical networks as well as two biological neural networks were explored with a three-state model of node activation for systematically varying levels of random background network stimulation. The results demonstrated that two principal topological aspects of hierarchical networks, node centrality and network modularity, correlate with the network activity patterns at different levels of spontaneous network activation. The approach further showed that the dynamic behavior of the cortical systems network in the cat is dominated by the network’s modular organization, while the activation behavior of the cellular neuronal network of Caenorhabditis elegans is strongly influenced by hub nodes. Generally, our results demonstrate the interaction of multiple topological features and dynamic states in the function of complex neural networks.


Complex networks Neural topology Modularity Betweenness centrality Cat Caenorhabditis elegans 


  1. 1.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science. 286 (1999) 509.CrossRefPubMedGoogle Scholar
  2. 2.
    Kaiser, M., Görner, M., Hilgetag, C.C.: Criticality of spreading dynamics in hierarchical cluster networks without inhibition. New J. Phys. 9 (2007) 110.CrossRefGoogle Scholar
  3. 3.
    Sporns, O.: Small-world connectivity, motif composition, and complexity of fractal neuronal connections. Biosystems. 85 (2006) 55.CrossRefPubMedGoogle Scholar
  4. 4.
    Bak, P., Chen, K., Tang, C.: A forest-fire model and some thoughts on turbulence. Phys. Lett. A. 147 (1990) 297; Drossel, B., Schwabl, F.: Self-organized critical forest-fire model. Phys. Rev. Lett. 69 (1992) 1629.CrossRefGoogle Scholar
  5. 5.
    Müller-Linow, M., Hilgetag, C.C., Hütt, M.T.: Organization of excitable dynamics in hierarchical biological networks. PLoS Comput. Biol. 4 (2008) e1000190.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Claus C. Hilgetag
    • 1
    • 2
    Email author
  • Mark Müller-Linow
    • 1
  • Marc-Thorsten Hütt
    • 1
  1. 1.School of Engineering and ScienceJacobs University BremenBremenGermany
  2. 2.Department of Health SciencesBoston UniversityBostonUSA

Personalised recommendations