Simulator-independent descriptions of connectivity in neuronal networks promise greater ease of model sharing, improved reproducibility of simulation results, and reduced programming effort for computational neuroscientists. However, until now, enabling the use of such descriptions in a given simulator in a computationally efficient way has entailed considerable work for simulator developers, which must be repeated for each new connectivity-generating library that is developed. We have developed a generic connection generator interface that provides a standard way to connect a connectivity-generating library to a simulator, such that one library can easily be replaced by another, according to the modeller's needs. We have used the connection generator interface to connect C++ and Python implementations of the connection-set algebra to the NEST simulator. We also demonstrate how the simulator-independent modelling framework PyNN can transparently take advantage of this, passing a connection description through to the simulator layer for rapid processing in C++ where a simulator supports the connection generator interface and falling-back to slower iteration in Python otherwise. A set of benchmarks demonstrates the good performance of the interface.