After a few days of thinking, I now realize that almost all of physical models commonly used for constructing the structure of molecules do not really use the microscopic force field of true molecules. The microscopic force field of a molecule is nothing but the repulsion between the electron pairs.The structure of physical model built from traditional balls and sticks does not obtain its structural stability from the repulsion between sticks. There is no interaction between these sticks in fact. As far as I can think of, our beaded molecule is probably the only physical model that really use the similar kind of pairwise hard-sphere repulsion to get the three-dimensional structure of the molecule. This is also the reason why the geometry of the beaded fullerene is in such a good agreement with that of the true molecule.
Right now, this approach only works for sp2-hybridized atoms. I guess it is possible to use beads to represent the repulsion interaction in the sp3-hybridized atoms, but it is probably not possible to generate the sp-type repulsion in the beaded network.