TABLE I.

Characteristics and epidemic thresholds of real-world networks. N is the network size, k_max is the maximum degree, r is the correlation coefficient of the degrees, ${\lambda }_c^{\mathit{H}\mathit{M}\mathit{F}}$ and ${\lambda }_c^{\mathit{Q}\mathit{M}\mathit{F}}$ are the HMF and QMF predictions for SIR, respectively, ${\lambda }_p^{\Delta }$(SIR) denotes the numerical threshold of SIR identified by Δ, and ${\lambda }_p^{\Delta }$(SIS) and ${\lambda }_p^{\chi }$(SIS) represent the numerical thresholds of SIS identified by Δ and χ, respectively.

Network	N	kmax	r	${\lambda }_c^{\mathit{H}\mathit{M}\mathit{F}}$	${\lambda }_c^{\mathit{Q}\mathit{M}\mathit{F}}$	${\lambda }_p^{\Delta }$(SIR)	${\lambda }_p^{\Delta }$(SIS)	${\lambda }_p^{\chi }$(SIS)
Hamsterster full35	2000	273	0.023	0.023	0.020	0.023	0.025	0.025
Brightkite36	56739	1134	0.010	0.016	0.010	0.014	0.012	0.012
arXiv astro-ph37	17903	504	0.201	0.015	0.011	0.012	0.012	0.012
Pretty good privacy38	10680	206	0.239	0.056	0.024	0.053	0.033	0.033
US power grid39	4941	19	0.003	0.348	0.134	0.446	0.261	0.264
Euroroad40	1039	10	0.090	0.479	0.249	0.498	0.331	0.331
Facebook (NIPS)41	2888	769	−0.668	0.004	0.036	0.075	0.079	0.077
Route views37	6474	1458	−0.182	0.006	0.022	0.037	0.034	0.036
CAIDA37	26475	2628	−0.195	0.004	0.014	0.019	0.019	0.019
email contacts42	12625	576	−0.387	0.009	0.02	0.027	0.024	0.025