FIG. 8.

Kendall's $\tau$ correlation coefficients evaluated between the actual spreading efficiency of the nodes and the rankings based on weighted coreness $s_s$ (red circles) as obtained by assigning asymmetric weighting $w_{ij}$ of Eq. (3) to the links and based on weighted coreness $s_s^{\prime }$ (black square) by assigning symmetric weighting $w_{ij}^{\prime }$ of Eq. (5) to the links. The necessity of invoking asymmetric weights is demonstrated by the higher accuracy in the ranking based on $s_s$ rather than on $s_s^{\prime }$. The real-world networks are (a) CA-Hep, (b) Astro, (c) Emailcontact, (d) PGP, (e) Blog, (f) AS, (g) Router, (h) Hamster, and (i) Netsci.