## 4 Implementation of the Proposed UniChain System
### Blockchain Initialization--Part II: Computing the Degree of a University Node
\[CM_{EAR}=\frac{\sum n1+n2+n5}{\sum n1+n2+n3+n5} \tag{3}\]  
\[CR_{EAR}=\frac{\sum n1}{\sum n1+n2+n4+n5} \tag{4}\]  
\[CN_{EAR}=1-\frac{\sum n5}{\sum n1+n2+n4+n5} \tag{5}\]  
Accordingly, the degree of a university \(i\) is computed by Equation (6):  
\[\delta_{i}=\sum_{EAR=1}^{m}Q_{EAR}=\sum_{EAR=1}^{m}L_{EAR}\;CM_{EAR}CN_{EAR}CR_ {EAR}NR_{EAR} \tag{6}\]  
For illustration, assume that a university would like to join the blockchain network. Assume that all universities that would like to join the blockchain network have to agree on 35 important items that should be included in an EAR and thus be measured for all EARs stored in their databases. Suppose that a university has two EARs, as detailed in Table 1. Table 2 shows how to compute the quality of the two academic records whose details are presented in Table 1. In Table 2, the EAR attributes, the quality of a record, and the degree of a university node are computed. At the end of the initialization stage, each university will have its degree that will be dynamically stored in the NC. Thus, the NC will automatically update the average degrees of nodes within the network as well as voter nodes. Note that a node with a degree that is greater than the average degree of the blockchain will be considered as a voter node, while the node that has the least degree among the nodes in the network will be assigned the task of generating the next new block. The proposal rewards the \"block's creator\" an incentive that will added to its degree to decrease its probability of recreating the next block instead of just creating a digital currency, thus achieving a fairness among universities and ensuring the sustainability of the system. \begin{table}
\begin{tabular}{c c c} \hline
**End****No.** & **L** & **CM** & **CR** \\ \hline \(1\) & \(\frac{35}{35}=1\) & \(\frac{35+7.5}{15+7.55}=0.84\) & \(\frac{15}{15+7.55}=0.50\) & \(1-\frac{5}{15+7.55}=0.83\) & \(\frac{30+1+1}{25}=0.92\) \\ \hline \(2\) & \(\frac{34}{35}=0.97\) & \(\frac{13+6.6}{12+6.77}=0.78\) & \(\frac{13}{13+6.37+6}=0.46\) & \(1-\frac{6}{13+6.37+6}=0.79\) & \(\frac{28+1+1}{35}=0.88\) \\ \hline \end{tabular}
\end{table} 
Table 2: An example of computing the quality of two academic records. \begin{table}
\begin{tabular}{c c c} \hline
**Indicator** & **EAR1** & **EAR2** \\ \hline L & 35 items are legal & 34 items are legal and one item is not authorized \\ \hline \(n_{1}\) & 15 correct elements & 13 correct elements \\ \hline \(n_{2}\) & 7 incorrect elements & 6 incorrect elements \\ \hline \(n_{3}\) & 5 missing elements & 7 missing elements \\ \hline \(n_{4}\) & 3 extra elements & 3 extra elements \\ \hline \(n_{5}\) & 5 conflict elements & 6 conflict elements \\ \hline \end{tabular}
\begin{tabular}{c c c} \hline
30 items are unique & 28 items are unique \\ \(NR\) & 2 items are shared with other 3 universities & 4 items are shared with other 3 universities \\ 3 items are shared with other 2 universities & 3 items are shared with other 2 universities \\ \hline \end{tabular}
\end{table} 
Table 1: Description of two academic records in a university node.