Table 2 Hybrid methods for the identification of influential spreaders in networks.

Method	Features	Subcrit.	Critical	Supercrit.
AD	\({c}_{AD}\)	1.000	1.000	1.000
	\(\langle {g}_{m}\rangle \)	0.993	0.961	0.931
	\(\langle {r}_{m}\rangle \)	0.755	0.548	0.119
CD	\({c}_{CD}\)	1.000	1.000	1.000
	\(\langle {g}_{m}\rangle \)	0.983	0.963	0.929
	\(\langle {r}_{m}\rangle \)	0.730	0.525	0.100
B	\({c}_{B}\)	1.000	1.000	1.000
	\(\langle {g}_{m}\rangle \)	0.946	0.954	0.938
	\(\langle {r}_{m}\rangle \)	0.590	0.483	0.110
AD,B	\({c}_{AD}\)	0.718	0.590	0.023
	\({c}_{B}\)	−0.027	0.046	0.069
	\(\langle {g}_{m}\rangle \)	0.987	0.964	0.936
	\(\langle {r}_{m}\rangle \)	0.755	0.551	0.116
AD,PR,LR	\({c}_{AD}\)	1.189	1.044	0.115
	\({c}_{PR}\)	−0.266	0.145	0.772
	\({c}_{LR}\)	−0.336	−0.632	−0.771
	\(\langle {g}_{m}\rangle \)	0.991	0.980	0.971
	\(\langle {r}_{m}\rangle \)	0.806	0.616	0.300
PR,LR,CD	\({c}_{PR}\)	0.006	0.386	0.803
	\({c}_{LR}\)	−0.419	−0.702	−0.771
	\({c}_{CD}\)	1.028	0.898	0.088
	\(\langle {g}_{m}\rangle \)	0.985	0.979	0.971
	\(\langle {r}_{m}\rangle \)	0.784	0.597	0.293
AD,B,LR	\({c}_{AD}\)	1.096	1.047	0.343
	\({c}_{B}\)	−0.010	0.067	0.083
	\({c}_{LR}\)	−0.466	−0.565	−0.395
	\(\langle {g}_{m}\rangle \)	0.993	0.976	0.952
	\(\langle {r}_{m}\rangle \)	0.810	0.625	0.220
PR,LR,EI	\({c}_{PR}\)	0.304	0.583	0.740
	\({c}_{LR}\)	0.101	−0.251	−0.733
	\({c}_{EI}\)	0.235	0.277	0.121
	\(\langle {g}_{m}\rangle \)	0.973	0.964	0.970
	\(\langle {r}_{m}\rangle \)	0.698	0.589	0.304

The table is organized in various blocks, each corresponding to a specific method. For every method m, either individual or hybrid, we report performance values for the three different dynamical regimes in terms of overall performance \(\langle {g}_{m}\rangle \) and overall precision \(\langle {r}_{m}\rangle \). The top three blocks correspond to the best individual methods in the three regimes according to overall performance metric. The remaining blocks are for hybrid methods. In each block, the first rows report values of the coefficient c_m of the individual method m in the definition of the hybrid method. We report the averages for the coefficient values over 1,000 iterations of the learning algorithm. The bottom two rows in each block correspond instead to the values of the performance metrics. Errors associated with all these measures are always smaller than 0.001, and they are omitted from the table for clarity.

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