Heat Kernel of Networks with Long-Range Interactions

Figure 8

The graphs G1 and G2 are co-spectral with respect to the traditional Laplacian but not co-spectral when considering the normalized Laplacian . Furthermore, they do not exhibit co-spectrality in relation to the normalized forms of (14) and (15), representing the Laplace and Mellin transforms of the -path Laplacian.

(a)

(b)