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Table 1 Quality of approximation of the count distribution for and . The empirical mean , variance , and cumulative distribution function have been obtained thanks to 10 000 random graphs. are the parameters of the Pólya-Aeppli distribution. and are the Kolmogorov-Smirnov distances. For then , is the quantile of the normal distribution (idem for the Pólya-Aeppli distribution).

From: Assessing the Exceptionality of Coloured Motifs in Networks

         

Motif

(%)

(%)

(%)

(%)

(%)

(%)

111

1023.65

27462.66

1021.97

27446.53

0.93

73.37

2.40

0.78

1407.4

1.6

1436

1.1

1533.9

0.23

1591

0.12

122

767.74

14941.43

766.05

14660.79

0.90

76.08

2.14

0.65

1047.7

1.5

1068

1.0

1140.2

0.25

1181

0.07

123

614.19

8546.68

615.26

8493.22

0.86

83.12

1.75

0.68

829.6

1.4

845

0.8

900.0

0.18

929

0.08

114

307.09

5729.89

307.77

5807.09

0.90

30.98

3.20

0.71

485.0

1.5

505

0.8

543.3

0.28

583

0.08

134

122.84

1305.02

123.06

1311.64

0.83

21.11

3.43

0.78

207.3

1.8

219

0.9

235.0

0.37

257

0.12

115

61.41

1180.68

61.72

1147.95

0.90

6.30

5.72

0.98

140.5

2.3

160

0.8

166.4

0.57

205

0.06

244

15.35

85.99

15.29

85.57

0.70

4.63

8.73

1.07

36.8

2.4

43

0.8

43.9

0.81

55

0.12

245

6.14

27.76

6.20

28.45

0.64

2.22

12.72

1.27

18.6

2.5

23

0.8

22.7

1.09

32

0.10

345

2.46

6.63

2.51

6.58

0.45

1.39

17.97

0.53

8.5

1.9

11

0.5

10.4

0.77

15

0.09

155

1.23

6.94

1.22

6.74

0.69

0.37

34.23

5.75

7.2

3.3

12

0.6

9.2

1.56

20

0.05

444

1.02

2.46

1.02

2.51

0.42

0.59

27.39

3.80

4.7

2.4

7

0.5

5.9

1.48

10

0.09

355

0.25

0.50

0.25

0.50

0.34

0.16

48.47

0.43

1.9

2.5

3

0.4

2.4

0.96

6

2e-05

455

0.12

0.20

0.13

0.20

0.23

0.09

51.63

0.16

1.2

0.6

2

0.1

1.5

0.65

4

0.03

555

0.008

0.01

0.007

0.008

0.035

0.007

52.61

2e-03

0.2

0.03

0

0.03

0.3

0.03

1

2e-05