Impact of Learning on the Structural Properties of Neural Networks

  • Branko Šter
  • Ivan Gabrijel
  • Andrej Dobnikar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4432)


We research the impact of the learning process of neural networks (NN) on the structural properties of the derived graphs. A type of recurrent neural network is used (GARNN). A graph is derived from a NN by defining a connection between any pair od nodes having weights in both directions above a certain threshold. We measured structural properties of graphs such as characteristic path lengths (L), clustering coefficients (C) and degree distributions (P). We found that well trained networks differ from badly trained ones in both L and C.


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  1. 1.
    Erdos, P., Renyi, A.: On random graphs. Publicationes Mathematicae 6, 290–297 (1995)MathSciNetGoogle Scholar
  2. 2.
    Watts, D.J.: Small Worlds. Princeton University Press, Princeton (1999)Google Scholar
  3. 3.
    Reka, A., Barabasi, A.L.: Statistical mechanics of complex networks. Reviews of modern physics 74, 47–97 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Letters to nature 393, 440–442 (1998)CrossRefGoogle Scholar
  5. 5.
    Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Advances in physics 51(4), 1079–1187 (2002)CrossRefGoogle Scholar
  6. 6.
    Bornholdt, S., Schuster, H.G.: Handbook of Graphs and Networks. Wiley-VCH, Weinheim (2003)zbMATHGoogle Scholar
  7. 7.
    Gabrijel, I., Dobnikar, A.: On-line identification and reconstruction of finite automata with generalized recurrent neural networks. Neural Networks 16, 101–120 (2003)CrossRefGoogle Scholar
  8. 8.
    Kim, J.B.: Performance of networks of artificial neurons: The role of clustering. Physical Review E 69, 045101/1-4 (2004)Google Scholar
  9. 9.
    Haykin, S.: Neural Networks. Prentice-Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  10. 10.
    McGraw, P.N., Menzinger, M.: Topology and computational performance of attractor neural networks. Physical Review E 68, 047102/1-4 (2003)Google Scholar
  11. 11.
    Torres, J.J., Munoz, M.A., Marro, J., Garrido, P.L.: Influence of topology on the performance of a neural network. Neurocomputing 58-60, 229–234 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Branko Šter
    • 1
  • Ivan Gabrijel
    • 1
  • Andrej Dobnikar
    • 1
  1. 1.Faculty of Computer and Information Science, University of Ljubljana, Tržaška 25, 1000 LjubljanaSlovenia

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