Generating complex connectivity structures for large-scale neural models

Abstract

Biological neural systems and the majority of other real-world networks have topologies significant different from fully or randomly connected structures, which are frequently applied for the definition of artificial neural networks (ANN). In this work we introduce a deterministic process generating strongly connected directed graphs of fractal dimension having connectivity structures very distinct compared with random or fully connected graphs. A sufficient criterion for the generation of strongly connected directed graphs is given and we indicate how the degree-distribution is determined. This allows a targeted generation of strongly connected directed graphs. Two methods for transforming directed graphs into ANN are introduced. A discussion on the importance of strongly connected digraphs and their fractal dimension in the context of artificial adaptive neural systems concludes this work.