  Neutrino masses and mixings can be generated in many different ways, with
some of these scenarios featuring new physics at energy scales relevant for
Large Hadron Collider searches. A systematic approach to constructing a large
class of models for Majorana neutrinos may be founded upon a list of
gauge-invariant effective operators -- formed from quarks, leptons and the
Higgs doublet -- that violate lepton-number conservation by two units. By
opening up these operators in all possible ways consistent with some minimality
assumptions, a complete catalogue of a class of minimal radiative neutrino mass
models may be produced. In this paper we present an analysis of Feynman diagram
topologies relevant for the ultra-violet completions of these effective
operators and collect these into a simple recipe that can be used to generate
radiative neutrino mass models. Since high mass-dimension effective operators
are suppressed by powers of the scale of new physics, many of the resulting
models can be meaningfully tested at the Large Hadron Collider.
