Figure 4.

The illustration of the persistent Betti numbers ${\beta }_q^{\alpha ,0}$ and the smallest nonzero eigenvalues of persistent Laplacians ${\lambda }_q^{\alpha ,0}$ against the radius α for the pentagon. The persistent Betti numbers are shown by the blue line. The smallest nonzero eigenvalues calculated by HERMES and Bertini are shown by a red line and red circles, respectively and one can see that they almost coincide. The half edge length is approximately sin(π/5) ≈ 0.58.