Using geometry to uncover relationships between isotropy, homogeneity, and modularity in cortical connectivity

Inferences of strong modular and hierarchical structure from some cortical network studies conflict with the broadly isotropic homogeneous connectivity that has been found to a first approximation in classical anatomical studies. This conflict is resolved via consideration of the geometry of the cortex. A new geometrically based connection matrix (CM) visualization method is used to better compare experimental CMs with model CMs and thereby minimize appearance of artifacts. Model networks based on spherical geometry containing similar isotropic, homogeneous connection distributions to the experiment are shown to reproduce, interrelate, and explain key properties of experimentally derived networks, such as clustering coefficient (CC), path length, mean degree, and modularity score, using only two parameters that are fitted to an experimental spatial connectivity distribution. A greater CC in the experiment than the model indicates that, while isotropy and homogeneity of connections is a good first approximation, connections at shorter range may exhibit additional perturbations that increase clustering. These geometrically based models provide a comparative framework to assist in the next stage of revealing and analyzing anisotropic and/or inhomogeneous connections in data and their effects on network properties and visualization.