Comparisons for the average number of internal DOF per vertex. The average number of internal DOF per vertex within the network for L = 20 are plotted as a function of fluctuating edge probability, p, based on Maxwell counting (red triangle), ensemble averaged PG (green cross), VPG (blue circle), and ensemble averaged bar-PG (purple square). The straight line is the lower bound estimate given by MCC. The VPG falls in between the PG and MCC results, which gives a much better approximation to the PG than MCC. The maximum error between the PG and VPG occurs at values of p close to the Maxwell rigidity transition.