Chapter

Parallel Processing and Applied Mathematics

Volume 7203 of the series Lecture Notes in Computer Science pp 511-520

Diameter of the Spike-Flow Graphs of Geometrical Neural Networks

  • Jaroslaw PiersaAffiliated withFaculty of Mathematics and Computer Science, Nicolaus Copernicus University

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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