Abstract: Many systems in nature are governed by a large number of agents that interact nonlinearly through complex feedback loops. When the networks are sufficiently large and interconnected, they typically exhibit self-organization and chaos. This talk describes the results of computer simulations of such large networks and shows the conditions under which chaos can be expected for an unweighted network of ordinary differential equations with sigmoidal nonlinearities and unit coupling. The largest Lyapunov exponent is used as the signature and measure of chaos, and the study includes the effects of damping, asymmetries in the distribution of coupling strengths, network symmetry, and sparseness of connections. Minimum conditions and optimal network architectures are determined for the existence of chaos. The results have implications to the design of social and other networks in the real world in which weak chaos is desired or as a way of understanding why certain networks might exist on the edge of chaos.