We often see normalized Laplacian spectra of graphs where density on eigenvalue 1 serves as an axis of symmetry, with particularly high (blue spectra in the figure) or low densities around this value (red spectrum in the figure).

1. What does high density on eigenvalue 1 (where 1 serves as an axis of symmetry) means in terms of graph structure (blue spectra)?
2. Similarly, what does low density on eigenvalue 1 (where 1 serves as an axis of symmetry, shaping a sort of rounded "M") means in terms of graph structure (red spectrum)?
3. Is their a known class of graphs which follows the shape described in question 2 (red spectrum)?

Any literature on the subject is appreciated.

We often see normalized Laplacian spectra of graphs where density on eigenvalue 1 serves as an axis of symmetry, with particularly high (blue spectra in the figure) or low densities (red spectrum) around this value.

1. What does a high density on eigenvalue 1 (where 1 serves as an axis of symmetry) means in terms of graph structure (blue spectra)?
2. Similarly, what does a low density on eigenvalue 1 (where 1 serves as an axis of symmetry, shaping a sort of rounded "M") means in terms of graph structure (red spectrum)?
3. Is their a known class of graphs which follows the shape described in question 2 (red spectrum)?

Any literature on the subject is appreciated.