"Take me to your Leaders" Networks

We rigorously define a most efficient network with n nodes and m arcs, as it regards network synchrony. Typically we assume that a node becomes active if it receives active input from at least t other nodes. This is followed by presenting a construction of families of networks that are most efficient. The resulting networks are "take me to your Leaders" networks of diameter 2. A discussion of advantages and disadvantages of using these networks in modeling is then anticipated.