Table 1 Statistics of single-layer networks and the aggregated (AGG.) network, including 1. the number of active nodes N^[α], i.e., nodes that are connected by at least one in-/out-link (Nicosia and Latora 2015); 2. the total number of edges E^[α]; 3. the average strength 〈s^[α]〉; 4. density D^[α] measuring the ratio of the number of edges to maximum possible number of edges; 5. fraction of nodes in the giant weakly connected component %G^[α]; 6. reciprocity r^[α] quantifying the likelihood of nodes with mutual links; 7. the Kendall’s τ correlation between in- and out-strengths \(\tau \left (s_{in}^{[\alpha ]}, s_{out}^{[\alpha ]}\right)\). 8. global clustering coefficient C^[α] which measures the extent that two neighbors of a node are connected; 9. assortativity coefficient by strength \(A_{s}^{[\alpha ]}\), i.e., the correlation between the out-strengths of source nodes and the in-strengths of destination nodes (Newman 2003)

N ^{[ α]}

9381

28,959

17,689

11,199

14,156

55,164

E ^{[ α]}

17,306

54,609

34,040

17,881

27,807

140,330

〈s^[α]〉

3.55

2.89

2.94

2.46

2.96

4.32

D ^{[ α]}

1.97 ×10⁻⁴

6.51 ×10⁻⁵

1.09 ×10⁻⁴

1.43 ×10⁻⁴

1.39 ×10⁻⁴

4.61 ×10⁻⁵

% G ^{[ α]}

76.55%

89.17%

83.84%

73.87%

88.87%

95.67%

r ^{[ α]}

0.24

0.19

0.36

0.45

0.33

0.29

\(\tau \left (s_{in}^{[\alpha ]}, s_{out}^{[\alpha ]}\right)\)

-0.06

-0.04

0.09

0.21

0.13

0.11

C ^{[ α]}

0.06

0.04

0.03

0.03

0.01

0.03

z(C^[α])

40.70

198.96

61.25

109.21

6.29

160.67

\(A_{s}^{[\alpha ]}\)

-0.08

-0.07

-0.1

-0.02

-0.08

-0.1

\(z\left (A_{s}^{[\alpha ]}\right)\)

-10.64

-17.24

-19.05

-4.60

-14.04

-37.80