## 5 Results
### Experiment on the Synthetic Datasets  
Experiments were carried out on the synthetic datasets to investigate the influencing factors of EQA process speed. We designed and performed experiments on different sizes of graphs and different numbers of vertex labels and edge labels of graphs. We could also further verify the effectiveness and scalability of EQA algorithms through the experiments. The synthetic datasets were generated by the graph data simulation generator used in [24]. The parameters of the simulation generator can be set by the users, including the number of edges, the number of vertex labels and the number of edge labels. As mentioned above, \(\overline{T}_{iso}\) and \(CT\) can evaluate the performance of the algorithms, and the trends were almost the same; however, \(CT\) was more stable. Therefore, \(CT\) was used in the experiments on the synthetic dataset as the evaluation criteria. We randomly selected 100 query positions for each dataset and calculated the average value of \(CT\) from the 100 experiments, denoted as \(\overline{CT}\). 1. Experiments on the increasing number of edges We investigated the influence of graph size on EQA process speed first. Keep the same number of vertex labels and edge labels, and increase the number of edges. The number of vertices was 3000; the number of edge labels was set as five; the number of vertex labels was set as five; and the number of edges was set as 6000, 7000, 8000 and 9000 separately. The experimental results are shown in Table 3. As can be seen from the table, \(\overline{CT}\) was increasing with the increasing number of edges, that is to say, the answering speed was decreasing. When the number of vertices in the graph was kept the same and the number of edges was increasing, the average degree of vertices was also increasing. Therefore, when searching the induced subgraph space in ascending order of the number of vertices, more candidate subgraphs would be generated in each layer, and more graphs would participate in the subgraph isomorphism testing; so the query time became longer, and the answering speed decreased. 2. Experiments on the increasing number of vertex labels We investigated the influence of vertex labels on EQA process speed subsequently. Keep the same  
Figure 12: Comparison results on the HPRD dataset. (**a**) The comparison of \(\overline{T}_{iso}\); (**b**) the comparison of \(CT\). size of graphs and the same number of edge labels, then increase the number of vertex labels. The graphs contained 3000 vertices and 8000 edges. The number of edge labels was set as five, and the number of vertex labels was set as 10, 30, 50 and 70 separately. The experimental results are shown in Table 4. As seen from the table, \(\overline{CT}\) was decreasing with the increasing number of vertex labels, that is to say, the answering speed was increasing. Since both the number of vertices and the number of edges in each graph were the same, the number of candidate subgraphs generated had little difference, as well as the number of candidate subgraphs participating in the isomorphism testing. However, with the increasing number of vertex labels, there were more unique induced subgraphs on the dataset and a higher probability to obtain MUIS earlier. Therefore, \(CT\) was decreasing, and the answering speed was increasing. 3. Experiments on the increasing number of edge labels We investigated the influence of edge labels on EQA process speed at last. Keep the same size of graphs and the same number of vertex labels, then increase the number of edge labels. All the graphs contained 3000 vertices and 8000 edges. The number of vertex labels was set as five, and the number of edge labels was set as 10, 30, 50 and 70 separately. The experimental results are shown in Table 5. As seen from the table, \(\overline{CT}\) was decreasing with the increasing number of edge labels, that is to say, the answering speed was increasing.