Table 3 Identification of influential spreaders in large networks.

Network	N	E	p _c	Ref.	url	\(\langle {{\boldsymbol{g}}}_{{\boldsymbol{ {\mathcal H} }}}\rangle /\langle {{\boldsymbol{g}}}_{{\boldsymbol{AD}}}\rangle \)
Network	N	E	p _c	Ref.	url	Subcrit.	Critical	Supercrit.
Slashdot	51,083	116,573	0.0262	^{44, 45}	url	1.003	1.017	1.062
Gnutella, Aug. 31, 2002	62,561	147,878	0.0956	^{46, 47}	url	1.009	1.040	1.039
Epinions	75,877	405,739	0.0062	^{45, 48}	url	1.012	1.057	1.130
Flickr	105,722	2,316,668	0.0142	^{45, 49}	url	1.007	1.082	1.242
Gowalla	196,591	950,327	0.0073	^{45, 50}	url	1.011	1.024	1.066
EU email	224,832	339,925	0.0119	^{45, 47}	url	1.002	1.009	0.923
Web Stanford	255,265	1,941,926	0.0598	⁵¹	url	1.009	1.031	1.035
Amazon, Mar. 2, 2003	262,111	899,792	0.0940	⁵²	url	1.008	1.025	0.994
YouTube friend. net.	1,134,890	2,987,624	0.0063	^{45, 53}	url	1.004	1.013	0.952
Average on large networks						1.007 ± 0.001	1.033 ± 0.007	1.050 ± 0.030
Average on the corpus of 100 networks						1.001 ± 0.002	1.021 ± 0.003	1.043 ± 0.005

We compare the performance of the hybrid method \( {\mathcal H} =\{{\rm{AD}},{\rm{PR}},{\rm{LR}}\}\) with the individual method AD. For the hybrid method, we use the values of the coefficients reported in Table 2. From left to right, we report the name of the network, number of nodes in the giant component, number of edges in the giant component, critical value p_c of the spreading probability, references to studies where the network was first analyzed, url where network data were downloaded, value of the ratio \(\langle {g}_{ {\mathcal H} }\rangle /\langle {g}_{AD}\rangle \) between the performance metric of the hybrid method \( {\mathcal H} =\{{\rm{AD}},{\rm{PR}},{\rm{LR}}\}\) and the one of the individual method AD for the subcritical, critical and supercritical regimes. The bottom two lines in the table report, for each dynamical regime, average values and standard errors of the mean for the ratios \(\langle {g}_{ {\mathcal H} }\rangle /\langle {g}_{AD}\rangle \) over the set of large networks and over the corpus of 100 networks considered in the rest of the paper.

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