# Measuring the Inferential Values of Relations in Knowledge Graphs
## 5 Experimental
### Analysis of Relation Connectivity  
As stated above, RIMIE employs the relation entropy to measure the inferential values of relations, and the high-entropy relations are considered crucial to the inference tasks on knowledge graphs. It is well known that in complex networks, the _connectivity_ of nodes and edges is regarded as an indicator of importance, mirroring the information-spreading capacity. Since knowledge graphs are a special class of complex networks, and knowledge reasoning can also be seen as a special kind of information spreading, it is necessary to explore the relationship between relation entropy and connectivity to further illustrate the effectiveness of RIMIE. The connectivity of a triple is defined as the sum of the degrees of the head and tail entities connected by the relation in the triple. Then, the connectivity of relations can be defined. The connectivity of a relation can be seen as the average connectivity of triples covering the relation. Triple connectivity and relation connectivity can be calculated by  
\[C\big{(}\big{(}h,r,t\big{)}\big{)}=degree(h)+degree(t) \tag{9}\]  
and  
\[C(r)=\frac{\sum\big{(}h,r,t\big{)}\in F^{r}C\Big{(}\big{(}h,r,t\big{)}\Big{)}} {|F^{r}|}, \tag{10}\]  
respectively, where \(F^{r}\) is the set of triples covering relation \(r\). For a set of relations, the average connectivity of relations in the set is defined as the connectivity of the relation set. The connectivity of the relation sets \"Random\", \"Max\", and \"REntropy\" is shown in Table 7.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Random** & **Max** & **REntropy** \\ \hline FB15K-237 & 850 & 368 & **927** \\ NELL-995 & 268 & 395 & **496** \\ YAGO3-10 & 66 & **11,847** & 906 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Relation Connectivity on FB15K-237, NLL-995, and YAGO3-10.  
Figure 8: Bar chart of the number of triples in the training set obtained after deleting four relations on FB15K-237, NELL-995, YAGO3-10.  
It can be observed that the connectivity of selected relations based on entropy is greater than that of the randomly selected ones, and it is also greater than the most frequently appearing relations in FB15k-237 and NELL-995. However, on the dataset YAGO3-10, it is only less than the connectivity of relations in the \"Max\" group. This is because YAGO3-10 contains a special relation called \"hasGender\". This relation has only two tail entities, namely \"male\" and \"female\", which are associated with all character entities in the graph. As a result, these two nodes have very high degrees, leading to a very high connectivity of the \"hasGender\" relation. Moreover, the \"hasGender\" relation increases the overall connectivity of relations in the \"Max\" group. Therefore, the connectivity of relations in the \"Max\" group in YAGO3-10 is greater than the other two groups. After the \"hasGender\" relation is removed, the connectivity of relations in the \"Max\" group is 626, which is less than the connectivity of relations in the \"REntropy\" group. Thus, it can be seen that the connectivity of relations selected based on entropy is greater, which is more conducive to information propagation. This indicates that RMIE can also effectively mirror the inferential value of relations from the perspective of connectivity.