7)

–12

1

0.16296515

8)

–8

–16

0.20221188

9)

–14

4

0.21201883

10)

–4

–15

0.22745032

11)

2

10

0.28359193

12)

3

6

0.39995134

13)

–5

5

0.41735257

14)

8

12

0.47586779

15)

7

13

0.49947027

16)

–18

9

0.85714941

17)

11

15

0.87457895

18)

14

17

1.73275734

19)

16

18

3.17333268

2.4 shows how the 20 amino acids were merged. The column

Height of Table 2.4 shows 19 merging heights in an ascending

aning that a subtree with a smaller distance was merged into this

ree in an earlier step and in a lower part of a tree. Every merge was

e., merging two amino acids or subtrees of amino acids. The column

Left of Table 2.4 stands for a lower-rank subtree or an amino acid

rged on the left side and the column named as Right of Table 2.4

r a lower-rank subtree or an amino acid to be merged on the right

r merging, a higher-rank subtree is generated. In these two columns,

e integer was used to index an amino acid and a positive integer was

ndex a previously generated lower-rank subtree. For instance, a

ne in the seventh row of the Right column stands for a lower-rank

the first merge between the amino acids R and Y. The height of this

as 0.067. The seventh merge happened between the 12^th amino acid

was −12) and the merged pair between the amino acids R and Y (the

r-rank subtree indexed by one) with the merging height 0.163. A

ging always produces a greater merging height. For instance, the

the first merge was 0.0670, the height of the second merge was

d the height of the seventh merge became 0.163.

R function cutree can be used to cut a hanging tree to generate

f it is required. It can cut a hanging tree to generate clusters by

the cluster number or deciding the maximum subtree height. The