Chemical Organisation Theory (COT) provides a way of understanding the evolution of collectively self-maintaining sets of molecular species. Adding conservation of matter to an Artificial Chemistry (AChem) can increase evolutionary activity, so it may be useful to understand the evolution of organisations under these conditions. We show how in a reaction network generated by a matter-conserving chemistry, every edge within an organisation must be a part of a cycle in the organisation’s bipartite representation. A consequence of this fact is used to alter an existing algorithm to more efficiently discover the complete set of organisations. The altered algorithm is shown to be faster than the original when tested on reaction networks generated by the Spiky-RBN AChem. Overall, this paper contributes useful tools for analysing chemical evolution in matter-conserving chemistries.