After finishing the catalysis process and recovering your catalyst, you will never get exactly the same mass balance. So, how can you prove that your cluster is the active catalyst, not a decomposed mononuclear species?
Its hard to definitively proove, but you can get evidence with in-situ spectroscopy and kinetics. Can you do the reaction in an NMR tube or at room temperature in an IR cell? You may be able to directly observe the cluster under catalytic conditions. You will need to show that the cluster and not a monomer is kinetically competent for the catalytic reaction. Once you isolate it from a reaction, can you put it back in a new flask with new substrate and will it catalyze the same reaction at the same rate? If so, then the cluster could be the catalyst.
The suggestion of Kyle is very reasonable, it is not simple to prove.
First, one has to distinguish between "single-species" and "multiple-species" catalytic systems. These catalytic systems require different analytic methods and experimental approaches for characterization. Indeed, it is very fascinating topic!
Recently we have prepared a short review on the topic:
Catalytic C-C and C-Heteroatom Bond Formation Reactions: In Situ Generated or Preformed Catalysts? Complicated Mechanistic Picture Behind Well-Known Experimental Procedures
This is an area where modeling can help. You can do IR or Raman in situ then use theory to figure out what modes they correspond to. This is very effective at figuring out, for example, whether a sorbate is on the atop or hole site; whether it's on an oxidized or reduced surface. The sorbate will also have distinctly different signature if it's on a cluster instead of mononuclear species
I can recommend this perfect book: Catalysis by Di- and Polynuclear Metal Cluster Complexes (Richard D. Adams, F. Albert Cotton, Wiley, 1998). There you can find general criteria for catalysis by clusters and polynuclear complexes. In brief they are follwoing:
1) If TOF increase when catalyst's concentration increase then cluster catalysis can take place.
2) If selectivity is different when mononuclear complexes are used as precursors instead of polynuclear compounds then cluster catalysis can take place.
3) If combination of some different metals catalyzes the reaction which is not catalyzed by these metals separately then heterometallic cluster catalysis can take place.
4) If reaction conditions can be modified to promote formation of metal-metal bond and that leads to increase of catalytic activity then cluster catalysis can take place.
5) If you have an asymmetric catalysis and asymmetry of the catalyst is specified by shape of metal core then most likely cluster catalysis takes place.
In the book you can find many examples and experimental methods for checking these points. For example, you can try to change catalyst's concentration or change a concentration of stabilizing ligand (pyridine, phosphine or something else that presents in the reaction mixture): if you decrease the concentration you promote formation of metal-metal bonds, if you increase an amount of ligand then you promote metal-metal bonds' cleavage, etc.
Anyway, you should take into account that you need to check as much criteria as possible to be sure about catalysis by cluster (and to prove it to your colleagues): your system must meet at least two criteria.