Recently, controllability of linear systems has been studied for various applications in large networks in biology, physics and engineering. To address scale and lack of precise knowledge of the network parameters issues, tools from structured system theory are well indicated. Due to the high dimension of the systems, and to the fact that only the graph of the network is known, but not the precise value of the relations between its components, the structured system theory is the natural and convenient approach for such study. Precisely, generic properties, i.e. properties that are true for almost all values of the parameters, can be stated. While most existing results concern networks of single integrators, in this paper, we show that generic controllability of a network of identical single-input-single-output controllable and observable systems is insured if and only if the structural controllability conditions are satisfied for the graph representing the network. This result constitutes an important generalization of the famous Lin's theorem stated in the seventies. It is even the broadest generalization of this theorem.