Function and form in networks of interacting agents

The main problem we address in this paper is whether function determines form when a society of agents organizes itself for some purpose or whether the organizing method is more important than the functionality in determining the structure of the ensemble. As an example, we use a neural network that learns the same function by two different learning methods. For sufficiently large networks, very different structures may indeed be obtained for the same functionality. Clustering, characteristic path length and hierarchy are structural differences, which in turn have implications on the robustness and adaptability of the networks. In networks, as opposed to simple graphs, the connections between the agents are not necessarily symmetric and may have positive or negative signs. New characteristic coefficients are introduced to characterize this richer connectivity structure.