<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def categorize_functional_groups(self, groups):
 """ Determine classes of functional groups present in a set. :param groups: Set of functional groups. :return: dict containing representations of the groups, the indices of where the group occurs in the MoleculeGraph, and how many of each type of group there is. """


        categories = {}

        em = iso.numerical_edge_match("weight", 1)
        nm = iso.categorical_node_match("specie", "C")

        for group in groups:
            atoms = [self.molecule[a] for a in group]
            species = [a.specie for a in atoms]
            coords = [a.coords for a in atoms]

            adaptor = BabelMolAdaptor(Molecule(species, coords))
            # Use Canonical SMILES to ensure uniqueness
            smiles = adaptor.pybel_mol.write("can").strip()

            if smiles in categories:
                this_subgraph = self.molgraph.graph.subgraph(list(group)).to_undirected()
                for other in categories[smiles]["groups"]:
                    other_subgraph = self.molgraph.graph.subgraph(list(other)).to_undirected()

                    if not nx.is_isomorphic(this_subgraph, other_subgraph,
                                            edge_match=em, node_match=nm):
                        break

                    if group not in categories[smiles]["groups"]:
                        categories[smiles]["groups"].append(group)
                        categories[smiles]["count"] += 1

            else:
                categories[smiles] = {"groups": [group],
                                      "count": 1}

        return categories