Table 6 Summary of structural characteristics of the Instances network before and after graph pruning. For each of the two graph pruning models, we tested under significance levels at 1% and 5%, which are indicated within brackets

#Nodes

6960

6454

6081

3949

3260

#Edges

216,504

97,141

68,100

19,208

12,849

Reciprocity

65.1%

57.9%

58.4%

67.8%

68.5%

Density

0.004

0.002

0.002

0.001

0.001

Average degree*

41.966

21.390

15.860

6.429

5.182

Average in-degree

31.107

15.051

11.199

4.864

3.941

% Sources

12%

13.1%

14.1%

24.1%

26.5%

% Sinks

6.6%

6.5%

6.7%

6.9%

7.9%

Degree assortativity*

− 0.274

− 0.249

− 0.224

− 0.244

− 0.272

Degree assortativity

− 0.253

− 0.231

− 0.214

− 0.253

− 0.283

Average path length

2.330

3.080

3.270

2.530

2.520

Diameter

5

6

7

5

6

Transitivity*

0.128

0.070

0.066

0.024

0.018

Clustering coefficient*

0.836

0.502

0.493

0.846

0.839

Clustering coefficient (full averaging)*

0.687

0.411

0.390

0.447

0.370

#Strongly connected components

1305

1276

1278

1228

1121

#Weakly connected components*

1

1

1

1

1

Modularity by Louvain*

0.289

0.495

0.540

0.469

0.495

#Communities by Louvain*

5 (5)

7 (7)

7 (7)

8 (8)

8 (9)

Modularity by Louvain**

0.353

0.442

0.442

0.369

0.375

#Communities by Louvain**

6 (8)

6 (8)

7 (9)

7 (9)

7 (11)

#Communities by Infomap**

6 (54)

10 (103)

12 (82)

6 (30)

5 (38)