Heat Kernel of Networks with Long-Range Interactions

Figure 16

Degree distributions of some realizations of ER random graphs having 1000 nodes each with different average degree and whose structure looks very similar. We will show that the derivative of the generalized heat content at the origin is able to distinguish these graphs. (a)  = 5. (b)  = 10. (c)  = 15. (d)  = 20.

(a)

(b)

(c)

(d)