This Technical Report introduces a data structure and an algorithm to efficiently to efficiently determine rigid clusters in a given molecule. This is a relevant problem in Monte Carlo simulations where the actuated DOFs change at each iteration. If the number of actuated DOFs is small, large temporary rigid groups appear during the time spanned by a MCS step. This document also provides a way of calculating the total energy in the molecules taking into account only inter-rigid energy terms. Thus, a large fraction of energy terms are not required to be computed, namely intra-rigid terms.