Heat Kernel of Networks with Long-Range Interactions

Figure 3

Illustration of the result of Lemma 4. We consider a Gilbert model for random graphs with nodes and connection probability (connected regime) generated using NetworkX [28] in Python. We then plot the generalized eigenvalues of the corresponding generalized Laplacian matrices (14) and (15) for . We observe that the eigenvalues of the generalized Laplacian matrix with the Mellin transform are greater (apart from , where they equal) compared to the corresponding eigenvalues of the generalized Laplacian matrix with Laplace transform.