# Toward Adaptability of E-Evaluation: Transformation from Tree-Based to Graph-Based Structure
## 4 Proposed Competence Tree Transformations to Graph-Based E-Evaluation Structure
### BTCG Transformation for Incremental Knowledge \(E\)-Evaluation
Figure 7: Result of BTCG transformation for the competence tree, presented in Figure 3 when all competencies except 2 nd level competencies 2, 3, and 4 are sequentially dependent. ```
1:\(root\) = root element of the competence tree
2:\(cPath\) = None
3:\(clast\) = None
4: BTCG(root, cPath, cLast)
5: BTCG(cComp, cPath, cLast):
6:if competence \(cComp\) has child competences then
7:for each child competence C of competence \(cComp\) (going from left to right) do
8:if competence \(C\) has no sequential dependency with sibling competences then
9:\(cPath\) = end of the test flow
10:endif
11: BTCG(C, cPath, cLast)
12:if\(clast\) == None then
13: add task \(T\) of competence \(cComp\) to the test flow
14:\(cLast\) = C
15:\(cPath\) = path from task \(T\)
16:else
17:if competence C has sequential dependency with sibling competences then
18: connect \(clast\) to new node \(D\) to indicate weather task \(T\) was solved correctly
19: add negative and positive paths for decision \(D\)
20:\(cPath\) = positive path of decision node \(D\)
21: add new task \(T\) of competence \(C\) to \(cPath\)
22:\(clast\) = C
23: merge positive and negative flows of \(cPath\)
24:else
25:if\(clast\) <> None then
26: connect \(clast\) to new node \(D\) to indicate weather task \(T\) was solved correctly
27: add negative and positive paths for decision \(D\)
28:\(cPath\) = positive path of decision node \(D\)
29: add new task \(T\) of competence \(C\) to \(cPath\)
30: merge positive and negative flows of \(cPath\)
31:\(cPath\) = end of the test flow
32:\(cLast\) = None
33:else
34: add new task \(T\) of competence \(C\) to \(cPath\)
35:endif
36:endif
37:endif
38:endfor
39:if competence C has no sequential dependency with sibling competences then
40: connect \(T\) to new node \(D\) to indicate whether all sibling tasks solved correctly
41: add negative and positive paths for decision \(D\)
42:\(cPath\) = positive path of decision node \(D\)
43: merge positive and negative flows of \(cPath\)
44:endif
45:endif
46:if\(clast\) == None then
47: add new decision node \(D\) to indicate whether task all sibling tasks solved correctly
48: add negative and positive paths for decision \(D\)
49:\(cPath\) = positive path of decision node \(D\)
50: add new task \(T\) of competence \(C\) to \(cPath\)
51: merge positive and negative flows of \(cPath\)
52:else
53: add task \(T\) of competence \(cComp\) to the \(cPath\)
54:endif
```  
**Algorithm 2** Pseudocode of BTCG transformation. The result of BTCG transformation demonstrates strong dependency on competence complexity, as well as sequential dependency between sibling competencies. Therefore, a different output might be generated depending on these two parameters and competence tree structure. The proposed transformations can convert any competence tree to a graph structure. However, for cases with no sequential dependencies and full sequential dependency, the generated graph structures will not ensure enough adaptability possibilities. This illustrates the transformation will not be enough for e-evaluation adaptability--the key factor is competence tree design. If all tasks have no relation and relative complexity, there will be no difference in how these tasks will be ordered into an e-evaluation system. Analysis of Transformation Results and Comparison to Contextual Graph to Practice Tree Transformation  
The results of the transformation might not be measured by one quantitative metric. Therefore, we summarize the transformation results with several different metrics. First of all, we measure the transformation results based on: (i) generated graph structure suitability for graph-based e-evaluation systems (does the graph starts with one action node and do all paths end up in one final node); and (ii) proportion between the number of task nodes in a graph-based e-evaluation structure and the number of task nodes in a competence tree e-evaluation structure.