A New Network Flow Platform for Building Artificial Neural Networks

  • Vassil Sgurev
  • Stanislav Drangajov
  • Vladimir JotsovEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 864)


A number of results are exposed in the present work, related to the transition being proposed from the widely spread nowadays platform for building up multilayer ANNs to a new platform, based on generalized network flows with gains and losses on directed graphs. It is shown that the network flow ANNs are of more general network structure than the multilayer ANNs and consequently all results obtained through the multilayer ANN are a part of the new network flow platform. A number of advantages of this new platform are pointed out. Generalized network flow with gains and losses is used in it as a base and on this ground, a mathematical model of ANN is proposed. A number of results are obtained for the network flow ANNs that are corollaries of the Ford-Fulkerson’s mincut-maxflow theorem, namely: existence of upper bound \(v_{max}\) of the flow from sources to consumers and lower bound \(c_{min}\) of capacity on all possible cuts, as well as equality between the maximal flow and the minimal cut. A way for building in additional linear constraints between the different signals in the ANN is pointed out. Defining of the optimal coefficients is carried out through corresponding optimization procedures with polynomial computational complexity of the network flow programming. The possibility for effective training and recognition is proven through rigorous procedures for the network flow platform and without using of heuristic algorithms for approximate solutions, characteristic to the multilayer ANNs.


Artificial neural networks Multilayer neural networks Network flow neural networks Mincut-maxflow theorem Network optimization procedures 


  1. 1.
    F. Rosenblatt, Principles of Neurodynamics (Spartan Books, N.Y, 1965)zbMATHGoogle Scholar
  2. 2.
    M. Minsky, S. Papert, Perceptrons (MIT Press, MA, 1969)zbMATHGoogle Scholar
  3. 3.
    T. Sejnowski, C. Rosenberg, Parallel networks that pronounce English text. Complex Syst. 1, 145–168 (1987)zbMATHGoogle Scholar
  4. 4.
    D. Graupe, Principles of Artificial Neural Networks, 3rd edn. Advanced series in circuits and systems, vol. 7 (World Scientific, 2013). ISBN 9814522740, 9789814522748Google Scholar
  5. 5.
    R.J. Schalkoff, Artificial Neural Networks (McGraw-Hill Higher Education, 1997). ISBN: 007057118XGoogle Scholar
  6. 6.
    D. Kwon, Intelligent machines that learn like children. Sci Am (2018).
  7. 7.
    V. Sgurev, Artificial Neural Networks as a Network Flow Capacities. Comptes Rendus de l’Academie Bulgare des Sciences, Tome 71(9) (2017)Google Scholar
  8. 8.
    L.R. Ford, D.R. Fulkerson, Flows in Networks (Princeton University Press, 1962)Google Scholar
  9. 9.
    N. Christofides, Graph Theory: An Algorithmic Approach (Academic Press, 1986)Google Scholar
  10. 10.
    P.A. Jensen, W.J.P. Barnes, Network Flow Programming (Krieger Pub Co, 1987). ISBN-13:978-0894642104, ISBN-10:0894642103.
  11. 11.
    D. Dai, W. Tan, H. Zhan, Understanding the Feedforward Artificial Neural Network Model From the Perspective of Network Flow (Cornell University Library, 2017).
  12. 12.
    V. Sgurev, S. Drangajov, V. Jotsov, Network flow interpretation of artificial neural networks, in Proceedings of the 9th International Conference on Intelligent Systems—IS’18, Madeira Island, Portugal, IEEEXplore (2019). ISBN: 978-1-5386-7097-2, ISSN: 1541-1672., 494-498
  13. 13.
    R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows: Theory, Algorithms, and Applications (Pearson 2013). ISBN 1292042702, 9781292042701Google Scholar
  14. 14.
    V. Sgurev, Network Flows with General Constraints (Publishing House of the Bulgarian Academy of Sciences, Sofia, 1991). (in Bulgarian)Google Scholar
  15. 15.
    V. Sgurev, St. Drangajov, Intelligent control of flows with risks on a network, in Proceedings of the 7th IEEE International Conference Intelligent Systems—IS’14, 24–26 Sept 2014, Warsaw, Poland, Tools, Architectures, Systems, Applications, vol. 2 (Springer International Publishing, Switzerland). Advances in Intelligent Systems and Computing, vol. 323 (2014), pp. 27–35

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Vassil Sgurev
    • 1
  • Stanislav Drangajov
    • 1
  • Vladimir Jotsov
    • 2
    Email author
  1. 1.Institute of Information and Communication TechnologiesBulgarian Academy of SciencesSofiaBulgaria
  2. 2.University of Library Studies and Information TechnologiesSofiaBulgaria

Personalised recommendations