## 3 Materials and Methods
### Methods
#### 3.3.2 Social Network Analysis  
We used a pathway matrix that identifies the interrelationship among the different authors. This allowed us to know the main actors in the network and permitted us to analyse each type of relationship identified separately. **Construction of a path matrix**. A matrix was constructed where the authors of the selected activity were crossed. A matrix was constructed by combining two by two all of the documents for the same statement for all of the authors. The result was a binary matrix, where 0 meant that there was no relationship of the selected type (C\({}_{i}\)) and 1 meant that on existed. A relationship was obtained when there was a C\({}_{i}\)-like collaboration between them in one or more of the selected documents (exercises). This matrix was used to identify the communities of authors for each type of collaboration. With the data from the path matrix, we constructed social network clusters of author collaborations based on undirected graphs. **Construction of the social network graph**. As already mentioned in Section 3.2.1, the _Author_behaviour_ function was computed from the average of all _intensity values_ of every pair of documents where the author was involved. Depending on the resulting average intensity, a _behaviour category_ was assigned to each author. Table 2 shows the boundaries and the interpretation of each _behaviour category_:  
Each relationship obeys a type of behaviour of a pair of authors with that pair of documents, which we describe as follows:  
* \(Q_{individuals}\): It corresponds to pairs of exercises that have a very low degree of similarity. They are from authors working individually. It is admitted that they have a certain similarity derived from having the same teacher and a similar programming style--a common background. This group included 59% of all the documents compared. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{\begin{tabular}{c} **Classification** \\ **Categories** \\ \end{tabular} } & \begin{tabular}{c} **Description** \\ **Description** \\ \end{tabular} & \
\begin{tabular}{c} **Relationship** \\ **between Documents** \\ \end{tabular} &
\begin{tabular}{c} **Intensity Value** \\ \end{tabular} \\ \hline \multirow{2}{*}{C\({}_{1}\)} & \multirow{2}{*}{No Relationship} & P1, P1 & 0 \\  & & P2, P1 & 0.25 \\ \hline \multirow{2}{*}{C\({}_{2}\)} & \multirow{2}{*}{Soft Relationship} & P3, P1 & 0.5 \\  & & P4, P1 & 0.75 \\  & & P2, P2 & 1 \\  & & P3, P2 & 1.25 \\ \hline \multirow{2}{*}{C\({}_{3}\)} & \multirow{2}{*}{Strong Relationship} & P4, P2 & 1.75 \\  & & P3, P3 & 2 \\ \hline \multirow{2}{*}{C\({}_{4}\)} & \multirow{2}{*}{Clear Copy} & P4, P3 & 2.5 \\  & & P4, P4 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Edges code (Similar_cod + Similar_intensity). \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{\begin{tabular}{c} **Similarity** \\ **Review Category** \\ \end{tabular} } & \begin{tabular}{c} **Interpretation** \\ \end{tabular} \\ \hline \(Q_{individuals}\) & [0.0–0.5] & \
\begin{tabular}{c} Each student coded separately \\ Authors studied together, shared \\ ways of coding but worked on \\ their own \\ \end{tabular} \\  &
\begin{tabular}{c} Authors shared a large amount of \\ code and tried hard to disguise it \\ by making changes \\ Authors engaged in dishonest \\ behaviour \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Authors behaviour category (_Author_behaviour_). \(\mathrm{Q}_{\mathrm{soft}}\): It corresponds to pairs of exercises that had similarities but in a slight way. We think that they were authors who asked their classmates when they were stuck, shared partial solutions but made the effort to understand the problem and solve it. It also corresponds to the fact that, in programming, some solutions are drawn from similar problems solved in class. This form of case-based learning or mutual help in a group is not a bad thing--quite the opposite.