  Following a newly introduced approach by Rasetti and Merelli we investigate
the possibility to extract topological information about the space where
interacting systems are modelled. From the statistical datum of their
observable quantities, like the correlation functions, we show how to
reconstruct the activities of their constitutive parts which embed the
topological information. The procedure is implemented on a class of polymer
models on hypergraphs with hard-core interactions. We show that the model
fulfils a set of iterative relations for the partition function that generalise
those introduced by Heilmann and Lieb for the monomer-dimer case. After
translating those relations into structural identities for the correlation
functions we use them to test the precision and the robustness of the inverse
problem. Finally the possible presence of a further interaction of peer-to-peer
type is considered and a criterion to discover it is identified.
