Recently attention has been paid to the identification of networks of linear time-invariant dynamical systems. One of the problems of interest is the identification of a particular transfer function within the network on the basis of available measurements. This raises the question of which signals need to be measured and which external excitation signals need to be present in the network in order to yield a consistent estimate of this desired transfer function. This paper examines the properties of the estimated transfer function in terms of bias error and variance error, for different models of the network. The main contribution is the derivation of sufficient richness conditions on the external signals for the consistent identification of the desired transfer function.