Heat Kernel of Networks with Long-Range Interactions

Figure 21

Time-dependent behavior of the derivative of the heat content at for Barabási–Albert (BA) graphs (represented by blue lines) and 5 Erdös–Rényi (ER) graphs (depicted by green lines). Each graph consists of 1000 nodes with an average degree ranging from 5 to 20. The derivative is computed based on the generalized Laplacian matrix using the Mellin transform. (a)  = 1. (b)  = 2. (c)  = 3. (d)  = 4.

(a)

(b)

(c)

(d)