0.**76 is a neighboring solution of solution find by Mitchell (see tab 2). We** try to explore the NN **by strictly increasing the Hamming distance from the** starting solution at each step of the walk. The neutral walk stops when there is no neutral step that increases distance. The maximum length of walk is thus 128. On average, the length of neutral walks on NN0.5 is 108.2 and 33.**1 on**
NN0.76. The diameter (see section 3.3.2) of NN0.5 **should probably be larger** than the one of NN0.76.

![0_image_0.png](0_image_0.png)

(a) (b)
Figure 6 shows the distribution of neutral degree collected along all **neutral**
walks. The distribution is close to normal for NN0.76. For NN0.5 **the distribution is skewed and approximately bimodal with a strong peak around 100 and**
a small peak around 32. The average of neutral degree on NN0.5 is 91.**6 and**
standard deviation is 16.6; on NN0.76, the average is 32.**7 and the standard**
deviation is 9.2. The neutral degree for NN0.5 is very high : 71.6 % of neighbors are neutral neighbors. For NN0.76, there is 25.**5 % of neutral neighbors. It**
can be compared to the average neutral degree overall neutral NKq**-landscape**
with N = 64, K = 2 and q = 2 which is 33.**3 % [41].**
Figure 7 gives an estimation of the autocorrelation function of neutral degree of the neutral networks. The autocorrelation function is computed for each neutral walk and the estimation r(k) of ρ(k**) is given by the average of** ri(k)
over all autocorrelation functions. For both NN, there is correlation. The correlation is higher for NN0.5 (ρ(1) = 0.85) than for NN0.76 (ρ(1) = 0.**49). From**
the autocorrelation of the neutral degree, one can conclude that the neutral network topology is not completely random, since otherwise correlation should have been nearly equal to zero. Moreover, the variation of neutral degree is smooth on NN; in other words, the neighbors in NN **have nearby neutral** degrees. So, there is some area where the neutral degree is homogeneous.