Generating Complex Connectivity Structures for Large-Scale Neural Models

Biological neural systems and the majority of other realworld 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.