Diameter of the Spike-Flow Graphs of Geometrical Neural Networks

  • Jaroslaw Piersa
Conference paper

DOI: 10.1007/978-3-642-31464-3_52

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7203)
Cite this paper as:
Piersa J. (2012) Diameter of the Spike-Flow Graphs of Geometrical Neural Networks. In: Wyrzykowski R., Dongarra J., Karczewski K., Waśniewski J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg

Abstract

Average path length is recognised as one of the vital characteristics of random graphs and complex networks. Despite a rather sparse structure, some cases were reported to have a relatively short lengths between every pair of nodes, making the whole network available in just several hops. This small-worldliness was reported in metabolic, social or linguistic networks and recently in the Internet. In this paper we present results concerning path length distribution and the diameter of the spike-flow graph obtained from dynamics of geometrically embedded neural networks. Numerical results confirm both short diameter and average path length of resulting activity graph. In addition to numerical results, we also discuss means of running simulations in a concurrent environment.

Keywords

geometrical neural networks path length distribution graph diameter small-worldliness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jaroslaw Piersa
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityTorunPoland

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