Heat Kernel of Networks with Long-Range Interactions

Figure 17

Degree distributions of some realizations of Barabási–Albert graphs whose having 1000 nodes 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 those graphs. (a)  = 5. (b)  = 10. (c)  = 15. (d)  = 20.

(a)

(b)

(c)

(d)