Optimal layering of neurons

Given the number of input, output, and hidden neurons in a neural network, what is the optimal layering of hidden neurons that will maximize the topological capacity of the neural network? Here we define the "topological capacity" of a neural network to be the number of connections between neurons. The answer to this question is very interesting. For hierarchical networks, having as many layers as possible is best; while for strictly layered networks, having one or two layers is best.