## 5 Evaluations
### Experiments on Layout Approach
#### 5.1.3 Quantitative Evaluation and Results Analysis  
**Result of network stability:** We computed statistics on the average displacements of nodes between adjacent layouts for different algorithms on three datasets to measure degrees of node movement between adjacent layouts. The results are presented in Table 2.  
As seen from the table, for average displacement, our algorithm outperforms FR algorithm, similar to Aging algorithm, and not as good as Incremental algorithm. Except for the McFarland dataset, the Incremental algorithm consistently achieves the smallest average displacement, aligning with the previous layout result analysis. The average displacement of our algorithm is larger than that of Incremental algorithm. This is because our algorithm makes some trade-offs on the impact of changes in network structure on the entire network.  
**Result of layout quality:** Finally, we assessed the layout quality of different algorithms. The results are presented in Tables 3-5 below.  
Based on the above layout quality metrics, except the email-Eu_day1 dataset, our algorithm produces layouts with the smallest number of edge crossings, and our algorithm also outperforms or closely matche the FR algorithm in terms of edge angle of incidence and shape similarity, indicating that our algorithm achieves better results in network layout quality. Incremental algorithm achieves best layout quality on the email-Eu_day1 dataset, highlighting its effectiveness for incremental data like email-Eu_day1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Network** & **Aging** & **FR** & **Incremental** & **Ours** \\ \hline Newcomb & 0.3388 & 0.3334 & 0.2860 & **0.3723** \\ McFarland & 0.5710 & **0.6498** & 0.5506 & 0.6040 \\ email-Eu & 0.7733 & 0.7725 & 0.7743 & **0.7848** \\ email-Eu_day1 & 0.81342 & 0.8203 & **0.8496** & 0.8165 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Edge angle of incidence metric. The best value for each metric is highlighted in bold.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Network** & **Aging** & **FR** & **Incremental** & **Ours** \\ \hline Newcomb & 2.6905 & 3.9169 & **1.0798** & 3.1675 \\ McFarland & 0.3969 & 1.0571 & 0.9594 & **0.3851** \\ email-Eu & 9.4554 & 15.1272 & **9.1390** & 12.1970 \\ email-Eu_day1 & 0.84235 & 6.1739 & **0.6715** & 4.5652 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average displacements. The best value for each metric is highlighted in bold.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Network** & **Aging** & **FR** & **Incremental** & **Ours** \\ \hline Newcomb & 0.3362 & **0.3812** & 0.2905 & 0.3515 \\ McFarland & 0.4292 & 0.2723 & 0.3526 & **0.4854** \\ email-Eu & 0.2289 & 0.2500 & 0.2838 & **0.3090** \\ email-Eu_day1 & 0.2928 & 0.3371 & **0.3916** & 0.3368 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Shape similarity metric. The best value for each metric is highlighted in bold.  
In summary, from both the layout result analysis in Section 5.1.2 and the quantitative metric analysis in Section 5.1.3, the SIPA algorithm achieves a balance between network stability and layout quality. Though the SIPA produces slightly larger node displacement between adjacent layouts than that of the Incremental and Aging algorithms, it brings chances for more nodes to seek ideal positions globally, thus better preserving overall structural shapes and relative positions within structures on significant network changes, and it presents better layout quality comparing to the other two algorithms with constraints.