A generic network is a resistor-inductor-capacitor (RLC) network which realises a set of impedance parameters of dimension one more than the number of elements in the network. We prove that such networks are minimal, in the sense that it is not possible to realise a set of impedance parameters of dimension n with fewer than n − 1 elements. We provide a necessary and sufficient condition for genericity in terms of the derivative of the mapping from element values to impedance parameters. We then prove that a network with a non-generic subnetwork is itself non-generic, and that any positive-real impedance can be realized by a generic network.