The Monte Carlo adaptation rule has been proposed to design asymmetric neural network. By adjusting the degree of the symmetry of the networks designed by this rule, the spurious memories or unwanted attractors of the networks can be suppressed completely. We have extended this rule to design full-connected neural networks and diluted neural networks. Comparing the dynamics of these two neural networks, the simulation results indicated that the performance of diluted neural network was poorer than the performance of full-connected neural network. As to this point, further research is needed. In this paper, we use the annealed dilution method to design a diluted neural network with fixed degree of dilution. By analyzing the dynamics of the diluted neural network, it is verified that asymmetric full-connected neural network do have significant advantages over the asymmetric diluted neural network.