Aspects of randomness in neural graph structures

• Published in: Biological cybernetics Vol. 108; no. 4; pp. 381 - 396
• Main Authors: Rudolph-Lilith, Michelle, Muller, Lyle E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-08-2014; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Animals; Applied sciences; Bioinformatics; Biological; Biological and medical sciences; Biomedical and Life Sciences; Biomedicine; Brain; Brain - anatomy & histology; Brain - physiology; Central nervous system; Cognitive Sciences; Combinatorics; Combinatorics. Ordered structures; Complex Systems; Computer Appl. in Life Sciences; Computer science; control theory; systems; Cybernetics; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General aspects; Graph theory; Graphs; Humans; Information retrieval. Graph; Life Sciences; Mathematics; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Models, Neurological; Nerve Net; Nerve Net - physiology; Nervous system; Networks; Neural Networks (Computer); Neural Pathways; Neural Pathways - anatomy & histology; Neural Pathways - physiology; Neurobiology; Neurons and Cognition; Neurosciences; Nonlinear Dynamics; Original Paper; Preprocessing; Psychology and behavior; Sciences and techniques of general use; Structural analysis; Theoretical computing; Vertebrates: nervous system and sense organs; Network structure; Network models; Scale-free graphs; Mammalian brain; Graph theory; Random graphs; Scale invariance; C. elegans; Prototype; Scale free; Nervous system; Neural network; Random distribution; History; Modeling; Subsampling; Random graph; Biological system; Graph connectivity; Network analysis; Bioinformatics; Functional network
• ISSN: 0340-1200; 1432-0770
• DOI: 10.1007/s00422-014-0606-6

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.