Figure 8:

Illustration of persistent spectral analysis of C₂₀ and C₆₀ using the spectra of ${\mathcal{L}}_q^{r+0}$ (q = 1, 2 and 3). (a) The number of zero eigenvalues of ${\mathcal{L}}_0^{r+0}$, i.e., ${\beta }_0^{r+0}$, under radius filtration. (b) The number of zero eigenvalues of ${\mathcal{L}}_1^{r+0}$, i.e., ${\beta }_1^{r+0}$ under radius filtration. (c) The number of zero eigenvalues of ${\mathcal{L}}_2^{r+0}$, i.e., ${\beta }_2^{r+0}$ under radius filtration. (d) The smallest non-zero eigenvalue ${\left({\tilde{\lambda }}_2\right)}_0^{r+0}$ under radius filtration. The radius grid spacing is 0.01 Å.