Before revision:  Here we analyze the stability and robustness of a large class of dynamical systems and demonstrate that the most hierarchical network structures, those equivalent to the total ordering, are the most robust. In particular, we determine the probability distribution of robustness over system connectivity and show that robustness is maximized by maximizing the number of links between strongly connected components of the graph representing the underlying system connectivity.
After revision:  Here we analyze the stability and robustness of a large class of dynamics on such networks. We determine the probability distribution of robustness over system connectivity and show that robustness is maximized by maximizing the number of links between strongly connected components of the graph representing the underlying system connectivity.