Weighted Clique Analysis Reveals Hierarchical Neuronal Network Dynamics

  • Paolo MasulliEmail author
  • Alessandro E. P. Villa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10613)


A biologically-plausible simulation of a neuronal network is studied as its topology is shaped by its activity by means of an encoding of its connectivity structure as a directed clique complex. Specially defined invariants of this mathematical structure, including the information about synaptic strength, are introduced and show how the initial topology of a network and its evolution during the simulation are tightly inter-related with the dynamical activity.


Recurrent neural dynamics Graph topology Directed clique complex Synfire chain Synaptic plasticity 



This work was partially supported by the Swiss National Science Foundation grant CR13I1-138032.


  1. 1.
    Bassett, D.S., Bullmore, E.T.: Small-world brain networks revisited. Neuroscientist 23(5), 499–516 (2016). doi: 10.1177/1073858416667720 CrossRefGoogle Scholar
  2. 2.
    Bonson, G.: The hierarchical organization of the central nervous system: implications for learning processes and critical periods in early development. Behav. Sci. 10, 7–25 (1965)CrossRefGoogle Scholar
  3. 3.
    Chaudhuri, R., Knoblauch, K., Gariel, M.A., Kennedy, H., Wang, X.J.: A large-scale circuit mechanism for hierarchical dynamical processing in the primate cortex. Neuron 88(2), 419–431 (2015)CrossRefGoogle Scholar
  4. 4.
    Del Prete, V., Martignon, L., Villa, A.E.: Detection of syntonies between multiple spike trains using a coarse-grain binarization of spike count distributions. Network 15(1), 13–28 (2004)CrossRefGoogle Scholar
  5. 5.
    Eguiluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V.: Scale-free brain functional networks. Phys. Rev. Lett. 94(1), 018102 (2005)CrossRefGoogle Scholar
  6. 6.
    Freeman, W.J.: Neural networks and chaos. J. Theor. Biol. 171, 13–18 (1994)CrossRefGoogle Scholar
  7. 7.
    Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar
  8. 8.
    Hilgetag, C.C., Hütt, M.T.: Hierarchical modular brain connectivity is a stretch for criticality. Trends Cogn. Sci. 18(3), 114–115 (2014)CrossRefGoogle Scholar
  9. 9.
    Hutchins, J.B., Barger, S.W.: Why neurons die: cell death in the nervous system. Anat. Rec. 253(3), 79–90 (1998)CrossRefGoogle Scholar
  10. 10.
    Iglesias, J., Villa, A.E.: Recurrent spatiotemporal firing patterns in large spiking neural networks with ontogenetic and epigenetic processes. J. Physiol. Paris 104(34), 137–146 (2010). Neural CodingCrossRefGoogle Scholar
  11. 11.
    Innocenti, G.M.: Exuberant development of connections, and its possible permissive role in cortical evolution. Trends Neurosci. 18(9), 397–402 (1995)CrossRefGoogle Scholar
  12. 12.
    Masulli, P., Villa, A.E.P.: The topology of the directed clique complex as a network invariant. Springer Plus 5, 388 (2016)CrossRefGoogle Scholar
  13. 13.
    Masulli, P., Villa, A.E.P.: Dynamics of evolving feed-forward neural networks and their topological invariants. In: Villa, A.E.P., Masulli, P., Pons Rivero, A.J. (eds.) ICANN 2016. LNCS, vol. 9886, pp. 99–106. Springer, Cham (2016). doi: 10.1007/978-3-319-44778-0_12 CrossRefGoogle Scholar
  14. 14.
    Park, H.J., Friston, K.: Structural and functional brain networks: from connections to cognition. Science 342(6158), 1238411 (2013)CrossRefGoogle Scholar
  15. 15.
    Tannenbaum, N.R., Burak, Y.: Shaping neural circuits by high order synaptic interactions. PLoS Comput. Biol. 12(8), 1–27 (2016)Google Scholar
  16. 16.
    Shaposhnyk, V., Villa, A.E.: Reciprocal projections in hierarchically organized evolvable neural circuits affect EEG-like signals. Brain Res. 1434, 266–276 (2012)CrossRefGoogle Scholar
  17. 17.
    Stam, C.J., Reijneveld, J.C.: Graph theoretical analysis of complex networks in the brain. Nonlinear Biomed. Phys. 1(1), 3 (2007)CrossRefGoogle Scholar
  18. 18.
    Yang, W., Sun, Q.Q.: Hierarchical organization of long-range circuits in the olfactory cortices. Physiol. Rep. 3(9), e12550 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.NeuroHeuristic Research GroupUniversity of LausanneLausanneSwitzerland

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