## 5 Results
### Experiment on the HPRD Dataset  
The HPRDdataset is provided by Human Proteinpedia, which was used in [40]. Human Proteinpedia is a community that shares and integrates human protein data. The dataset has 9460 vertices, 37,081 edges and 301 different vertex labels. The average degree for each vertex is seven, and the maximum degree is 249.  
During the process, 15 query points were randomly selected to conduct the experiments. Similar information as the YEAST dataset is shown in Table 2. Both the baseline and EQA algorithms can complete the MUIS query process on the HPRD dataset.  
Comparing Tables 2 and 1, it can be found that the number of vertices of MUIS found on the HPRD dataset was less than that of MUIS found on the YEAST dataset in most cases. That is to say, less layers were searched to find MUIS on the HPRD dataset. This indicates that the time to answer MUIS query on the HPRD dataset was less than that on the YEAST dataset in some sense.  
Figure 12a,b shows the comparison of \(\overline{T}_{iso}\) and \(CT\) of the baseline and EQA algorithms separately. The meaning of the X-axis and Y-axis of Figure 12 is the same as that of Figure 11.  
According to the two criteria \(\overline{T}_{iso}\) and \(CT\) shown in Figure 12, the performance of EQA was better than that of the baseline algorithm. Comparing Figure 11 with Figure 12, we find that the time to query MUIS on the HPRD dataset was usually less than that on the YEAST dataset, which was the same as the conclusion observed in Table 2. On the HPRD dataset, in many cases, both the baseline and EQA algorithms have less query time, so the performance advantage of EQA was not as obvious as that on the Yeast dataset. This further verifies the above-mentioned conclusion: in the MUIS query process, the longer \(\overline{T}_{iso}\), or the more \(CT\), the greater advantage of EQA over the baseline algorithm.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**\#** & **Query Position** & **Vertex \#** & **MUIS** \\ \hline \#1 & 1890 & 4 & 100 568 723 1890 \\ \#2 & 2155 & 3 & 134 2155 2157 \\ \#3 & 2977 & 2 & 1098 2977 \\ \#4 & 3434 & 4 & 236 239 3434 6928 \\ \#5 & 3789 & 3 & 1144 3789 4832 \\ \#6 & 4334 & 3 & 69 4334 4677 \\ \#7 & 4567 & 4 & 87 2734 4567 4569 \\ \#8 & 5332 & 4 & 77 153 235 5332 \\ \#9 & 5347 & 5 & 269 346 347 349 5347 \\ \#10 & 5701 & 4 & 659 2255 5701 6596 \\ \#11 & 5734 & 3 & 5734 5767 5768 \\ \#12 & 6758 & 4 & 419 1282 1818 6758 \\ \#13 & 7345 & 4 & 1686 3142 3840 7345 \\ \#14 & 8434 & 3 & 127 2959 8434 \\ \#15 & 9147 & 4 & 1457 1728 3277 9417 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental results on the HPRDdataset.  
Figure 11: Comparison results on the YEAST dataset. **(a)** The comparison of \(\overline{T}_{iso}\); **(b)** the comparison of \(CT\). EQA, Efficient Query Answering.  
The reason for this phenomenon is speculated as follows. Although both the number of vertices and the number edges of the HPRD dataset were significantly larger than those of the YEAST dataset, the average degrees of the vertices of the two datasets had little difference. As a result, there was little difference between the number of induced subgraphs generated by the layer with the same number of vertices, as well as the number of candidate MUISs that needed to execute the isomorphism testing. However, the number of vertex labels in the HPRD dataset was significantly more than the number of vertex labels in the YEAST dataset, so on the HPRD dataset, the isomorphism testing was faster, and there were more unique induced subgraphs and a higher probability to obtain MUIS earlier. Therefore, the query time on the HPRD dataset was relatively shorter. Experiments on the synthetic dataset will further verify the above speculation.