We present a method that is based on the Ladd-Frenkel (LF) thermodynamic integration for the study of the rigidity of networks of particles bonded together by short-ranged square well attractive potentials. We show that, by taking the limit of the attractive range going to zero, the celebrated Baxter limit, the degrees of freedom per particle of the system reduces to the fraction of floppy modes, i.e.those modes associated with movements at constant bonding distance. This method allows us to enumerate this fraction in a straightforward way and to calculate precisely the entropy associated with the sampling of phase space due to these floppy modes. Inparticular, we shall discuss how this quantity changes in the case of three (3D) and two dimensions (2D). © 2008 IOP Publishing Ltd.