Monte Carlo simulations of linear and cyclic alkanes were performed on a coarse-grained high coordination lattice. The simulations were performed at 473 K for CNH2N+2 and CNH2N where N had the values of 60, 100, and 316. The results indicated: (i) at low molecular weights, cyclic alkanes have lower diffusion coefficients than linear alkanes, and (ii) at high molecular weights, they have higher diffusion coefficients than linear alkanes. The lower diffusion coefficient of the small cyclic alkanes was attributed to the high local density within the volume defined by the smaller mean square radius of gyration of the cyclic alkanes. The high local density of cyclic alkane segments resulted in a decrease in the mobility of the beads. The crossover in diffusion coefficients was observed around the entanglement molecular weight of linear alkanes, which suggests that the linear alkanes are more susceptible to the effects of entanglements than are the cyclic alkanes.