Biological Cybernetics

, Volume 108, Issue 4, pp 381–396 | Cite as

Aspects of randomness in neural graph structures

  • Michelle Rudolph-LilithEmail author
  • Lyle E. Muller
Original Paper


In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural systems, however, a few moderately robust experimental reconstructions have been reported, and these have long served as fundamental prototypes for studying connectivity patterns in the nervous system. In this paper, we provide a comparative analysis of these “historical” graphs, both in their directed (original) and symmetrized (a common preprocessing step) forms, and provide a set of measures that can be consistently applied across graphs (directed or undirected, with or without self-loops). We focus on simple structural characterizations of network connectivity and find that in many measures, the networks studied are captured by simple random graph models. In a few key measures, however, we observe a marked departure from the random graph prediction. Our results suggest that the mechanism of graph formation in the networks studied is not well captured by existing abstract graph models in their first- and second-order connectivity.


Graph theory Network structure Random graphs  Scale-free graphs Mammalian brain C. elegans Network models 



The authors wish to thank OD Little for inspiring comments and A Destexhe for continuing support. Work supported by the CNRS and the European Community (BrainScales project, FP7-269921). LM is a PhD fellow from École des Neurosciences de Paris (ENP).

Supplementary material

422_2014_606_MOESM1_ESM.pdf (917 kb)
Supplementary material 1 (pdf 917 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.CNRSUnité de Neurosciences, Information et Complexité (UNIC)Gif-sur-YvetteFrance

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