In this note, necessary and sufficient rank conditions are proposed for checking the strong structural controllability of structured networks with identical nodes. More specifically, for a network with multi-input multi-output (MIMO) nodes, under an assumption called the strong invertibility for the nodal systems, the strong structural controllability of a given structured network is shown to be solely determined by its own topology. For the single-input single-output (SISO) case, such an assumption is allowed to be dropped by incorporating certain controllability and observability conditions for the nodal systems. Additionally, we utilize a recently developed graph-theoretical method for structured systems to verify the proposed rank conditions.