On Some Input-Output Dynamic Properties of Complex Networks

In this brief, we obtain the relationship between dynamic properties of system and network structures of complex networks. We show that the sum of the product of weights of the shortest paths between control and output nodes is equal to the gain factor of the pole-zero-gain transfer function of the complex network. We also show that dc-gain for the peripheral nodes of the complex network depends on the distance between the control and output nodes in the network. Existence of non-minimum phase zeros for collocated control and output nodes is discussed. The theoretical developments are verified using IEEE-4 bus power networked system application.