# 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  
The BTCG transformation is similar to the inversion of the TBCG--tasks are presented to students from the lowest complexity to greater complexity, and only if the task is solved correctly (in TBCG transformation additional tasks were given if the student fails the task). While the task sequence in the case of all success cases in the BTCG transformation is identical to the inverted order results of the TBCG transformation in the case of all fail cases (see Figure 5), the graph structure cannot be obtained by changing the order of the graph. To implement BTCG transformation, the start point is the leftmost and lowest node in the competence tree, illustrating the task of lowest complexity (see node 11 in Figure 3). If a student fails the task, the sequential dependency between sibling competencies in the tree structure must be inspected. If the sequential dependency exists at the same level, it means the student is missing essential knowledge to move further with a more difficult task, and the evaluation will be finished (as a result, material related to this missing competence will be provided for the student to obtain the needed competencies). If sequential dependency at this level does not exist, sibling competence tasks (node 12 in Figure 3) will be presented for the student to solve; however, the parent competence task (node 5 in Figure 3) will not be given to the student. This is based on the idea that, without having some competence, the student will not be able to solve more difficult tasks, which include the missing competence as one of the elements in the task's solution. Whether the evaluation finishes after at least one fail in one level of the competency tree depends on sequential dependency in the tree structure. By recursively analyzing the  
Figure 5: A transformation process: (**a**) TBCG where all a student’s answers are incorrect (tasks sequence is 1, 3, 7, 10, 9, 8, 6, 2, 5, 4); (**b**) BTCG where all a student’s answers are correct (tasks sequence is 4, 5, 2, 6, 8, 9, 10, 7, 3, 1). parent competencies, if a competency with non-sequential dependency child competencies exists, the evaluation will not be finished. It means other competencies are independent of the ones the student failed. Therefore, it can be evaluated in the same test. Therefore, when competency with non-sequential dependency child competencies is indicated in the path to root competency, the lowest level (the most left bottom level) competency task of such competency will be added (node 7 in Figure 3, if only node 1 has sequentially independent competencies 2, 3 and 4) to the test as an additional element in the graph. Success means the student has the competence; therefore, more difficult tasks can be given to him or her. As such, if there is a sibling competence task in the right, it will be given to the student (see node 12 in Figure 3), regardless of whether it is sequentially independent or not. If there are no additional sibling competencies in the right, the parent competence task (node 5 in Figure 3) should be analyzed for presentation in the test. However, the parent competency task will be included in the test only if all child competence tasks are solved correctly. If at least one child competence task is unsuccessfully solved, it means some competencies are missing to solve the parent competence task. All the processes are repeated recursively for each competency included in the graph-based e-evaluation solution. The BTCG pseudocode is presented in Algorithm 2. Transformation results for the competence tree (presented in Figure 3), when all competencies are sequentially dependent, are presented in Figure 6. When all competencies except second level competencies (nodes 2, 3, and 4 in Figure 3) are sequentially independent, they are transformed to different graph-based structures. The results are presented in Figure 7.  
Figure 6: Result of BTCG transformation for the competence tree, presented in Figure 3 when all competencies are sequentially dependent.