We extend the connection graph stability method, originally developed for symmetrically
coupled networks, to the general asymmetrical case. The principal new component of the
method is the transformation of the directed connection graph into an undirected graph. The
extension of the method to asymmetrical coupling consists in symmetrizing the graph and
associating a weight to each path. This weight involves the node unbalance of the two
nodes. The synchronization condition for this symmetrized-and-weighted network then also …