Spectral clustering result interpretation
Supposedly because of the weighting / normalization.

Point 8 is fairly far from all it's neighbors, so it's edges have a similar weight; and the normalization increases the edge weight to give every point the same influence. It's two other cluster members are (except they have one neighbor) similar. So I wouldn't be surprised if the two strongest edges after normalization of 8 are to 1 and 2.

To understand this better, I suggest that you compute the affinity matrix and visualize the affinities as edge strengths. The spectral embedding may also be worth looking at.

But this is an interesting example about the drawbacks of spectral clustering: normalization may give too much weight on "outliers".