For our initial analyses [21],[22],[32] graphs in child and adult groups were presented in either a pseudo-anatomical fashion or in their actual 3D positions (in Talairach space). Here we add another representation often used in graph theory - spring embedding. In this procedure, a spring constant is added to all of the connections in the network allowing for the pairwise regional connections to relax to their lowest energetic state. The algorithm applied in the present analysis is known as Kamada-Kawai [45] - one of the most commonly used strategies for displaying graph network data. In brief, each functional connection between a pair of nodes is treated as a spring with a spring constant related to the strength of the specific correlation. The nodes are then randomly placed in a plane, which places high strain on the “spring-loaded” connections. The algorithm then iteratively adjusts the positions of each node to reduce the total energy of the system to a minimum. As the pair-wise connections relax to their lowest energetic states the “natural” configuration of the network is revealed. By observing multiple
