Structural analysis of neural circuits using the theory of directed graphs

A new approach to analysis of structural properties of biological neural circuits is proposed based on their representation in the form of abstract structures called directed graphs. To exemplify this methodology, structural properties of a biological neural network and randomly wired circuits (RC) were compared. The analyzed biological circuit (BC) represented a sample of 39 neural nuclei which are responsible for the control of the cardiovascular function in higher vertebrates. Initially, direct connections of both circuits were stored in a square matrix format. Then, standard algorithms derived from the theory of directed graphs were applied to analyze the pathways of the circuits according to their length (in number of synapses), degree of connectedness, and structural strength. Thus, the BC was characterized by the presence of short, reciprocal, and unidirectional pathways which presented a high degree of heterogeneity in their strengths. This heterogeneity was mainly due to the existence of a small cluster of reciprocally connected neural nuclei in the circuit that have access, through short pathways, to most of the network. On the other hand, RCs were characterized by the presence of long and mainly reciprocal pathways which showed lower and absolute homogeneous strengths. Through this study the proposed methodology was demonstrated to be a simple and efficient way to store, analyze, and compare basic neuroanatomical information.