  We study the transport of information between two complex networks with
similar properties. Both networks generate non-Poisson renewal fluctuations
with a power-law spectrum 1/f^(3-\mu), the case \mu= 2 corresponding to ideal
1/f-noise. We denote by \mu_S and \mu_P the power-law indexes of the network
"system" of interest S and the perturbing network P respectively. By adopting a
generalized fluctuation-dissipation theorem (FDT) we show that the ideal
condition of 1/f-noise for both networks corresponds to maximal information
transport. We prove that to make the network S respond when \mu_S < 2 we have
to set the condition \mu_P < 2. In the latter case, if \mu_P < \mu_S, the
system S inherits the relaxation properties of the perturbing network. In the
case where \mu_P > 2, no response and no information transmission occurs in the
long-time limit. We consider two possible generalizations of the
fluctuation-dissipation theorem and show that both lead to maximal information
transport in the condition of 1/f-noise.
