Table 3 Tieness for each case study and an extra case study representing the situation when NO and coAfrequency are in accordance

Case 1: a pair of researchers

Fig. 1

0

2

0.0425

without any common neighbor

Case 2: determining if two researchers

Fig. 2 a

0

5

0.0375

are from the same community or not

Case 2: determining if two researchers are

Fig. 2 b

0.33

5

0.115

from the same community or not

Case 3: little collaboration between a pair of

Fig. 3

0.5

2

0.1425

researchers and a plenty of common neighbors

Case 4: results with extreme values

Fig. 4 a

1

3

0.2565

Case 4: results with extreme values

Fig. 4 b

0

40

0.25

Regular Case: NO and coAfrequency

Fig. 3 with w=12

0.5

12

0.18

in agreement