Table 5 Emphasized influential, prominent, and dual concepts and representations.

From: Using social network analysis to investigate mathematical connections in U.S. and Chinese textbook problems

Network

PEP-A

UCSMP

Vertex

In

Out

%

I:O

Rating

Vertex

In

Out

%

I:O

Rating

Original

Circle

64

53

9.7

1.2

Dual

Circle

46

38

9.9

1.2

Dual

Ellipse

51

38

7.4

1.3

Dual

Ellipse

21

61

9.7

0.3

Infl

Hyperbola

46

36

6.8

1.3

Dual

Hyperbola

25

32

6.7

0.8

Dual

Center

39

28

5.5

1.4

Dual

Radius

22

19

4.8

1.2

Dual

Parabola

28

37

5.4

0.8

Dual

Parabola

13

25

4.5

0.5

Infl

Line

42

16

4.8

2.6

Pro

Two INT

19

2

2.5

9.5

Pro

Circle; G

8

0

19.0

/

Pro

Circle; S1

2

16

11.4

0.1

Infl

Parabola; G

6

0

14.3

/

Pro

Ellipse; G

8

4

7.6

2.0

Pro

Circle; S2

0

6

14.3

0.0

Infl

Hyperbola; S1

0

9

5.7

0

Infl

Parabola; S1

0

6

14.3

0.0

Infl

Circle; G

8

0

5.1

/

Pro

      

Hyperbola; G

8

0

5.1

/

Pro

Schema-based

Ellipse

21

15

7.4

1.4

Dual

Ellipse

9

21

8.0

0.4

Infl

Line

20

8

5.7

2.5

Pro

Circle

14

15

7.8

0.9

Dual

Hyperbola

19

9

5.7

2.1

Pro

Circle; S1

1

4

3.2

0.3

Infl

  1. Note. % stands for centrality (original) and connectivity (schema-based); I:O In:Out, Infl Influential, Pro Prominent, INT intersections. Considering the connection network in each series, the top 5 concepts and representations (with concepts) are bolded in terms of in- and out-degree, respectively. For the schema-based network in each series, the top 2 concepts and representations (with concepts) are bolded based on in- and out-connection, respectively. Vertices with 0 to 3 for in-/out-degree/connection are not included here due to their minimal effect on the whole network .
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