Table 1 Assortativity coefficient for the ensembles of different real networks, the maximal degree and the structural cut–off degrees. The table shows the structural cut–off k_cut obtained from Eq. (27), \(\sqrt{N\langle k\rangle }\) and from Eq. (28). Their values are only shown if they are smaller than the maximal degree \({k}_{\max }\).

Network	ρ_d	ρ_ME1	ρ_ME2	ρ_ME3	\({{\boldsymbol{k}}}_{{\bf{\max }}}\)	\({{\boldsymbol{k}}}_{{{\boldsymbol{r}}}_{{\bf{\max }}}}\)	\(\sqrt{{\boldsymbol{N}}{\boldsymbol{\langle }}{\boldsymbol{k}}{\boldsymbol{\rangle }}}\)	\({{\boldsymbol{k}}}_{{{\boldsymbol{j}}}_{{\bf{\max }}}}\)
Adj nouns	−0.129	−0.125	−0.085	−0.047	49	28	29.15	15
Airports	−0.267	−0.223	−0.264	−0.017	145	64	77.20	91
Astro	0.235	0.254	−0.002	0.000	360	—	—	—
C. elegans	−0.091	−0.035	−0.030	−0.017	93	56	67.68	32
Dolphins	−0.043	−0.027	−0.050	−0.045	12	—	—	—
Football	0.162	0.136	−0.024	−0.005	12	—	—	—
Hep-Th	0.293	0.321	−0.012	0.032	50	—	—	—
AS-Internet	−0.194	−0.188	−0.176	−0.042	2389	116	216.37	1334
Karate	−0.475	−0.434	−0.205	−0.114	17	12	12.49	12
Net Sci	−0.081	−0.025	−0.018	−0.010	34	—	—	—
Political blogs	−0.221	−0.153	−0.046	−0.007	351	149	182.86	116
Political books	−0.127	−0.135	−0.021	−0.018	25	—	—	—
Power	0.003	0.035	−0.022	0.030	19	—	—	—
Protein	−0.136	−0.080	−0.007	−0.005	282	147	172.31	46
Random ER	−0.004	−0.002	−0.012	0.035	13	—	—	—
Les Mis	−0.165	0.005	−0.079	−0.065	36	19	22.54	15

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