## 5 Evaluations
### Experiments on Layout Approach
#### 5.1.2 Layout Result Analysis  
Firstly, we present layout results of the three datasets usingour algorithm considers the structural-based influence on different nodes, the node 7 has a greater degree of freedom, while the other nodes is reduced, resulting in smaller positional changes. When the network updates from the fourth state to the fifth state and adds back previously deleted node 14, the shape of this structure undergoes significant changes in the layout generated by all algorithms except for our algorithm. **Analysis on The Newcomb Dataset:** For the Newcomb dataset, Figure 11 displays the layout results for the first ten consecutive states under different algorithms. Unlike the McFarland dataset, the Newcomb dataset maintains a consistent number of nodes across all states, and the variations in the network structure are solely attributed to changes in edges. From the above layout result, the Incremental algorithm exhibits better stability than the other three algorithms across all time frames though there are substantial changes in actual network; Only the Incremental algorithm and our algorithm preserve the relative positions of nodes within the structure for some structure changes (as the example highlighted portions in states 6-9). We elaborate the detailed analysis as follows. First, when considering the overall layout shapes, the Incremental algorithm exhibits relatively consistent layout shapes across all time frames, while the layouts generated by the other algorithms undergo more significant changes. However, it's important to note that the actual network structure experiences substantial changes itself, and the Incremental algorithm excessively restricts node movement, resulting in layouts that do not effectively reflect the network's structural changes. Figure 10: Layout result comparison based on McFarland data. Node 12 and node 5 are highlighted with red and blue circles, their spatial and relative positions are kept stable in our algorithm and the incremental algorithm, but changes in the other two algorithms. The shape of the blue-color-highlighted structure is better preserved with our algorithm on significant change (step 4) and on adding back a node (step 5). Second, for some structures with minor changes, such as the highlighted portions in states 6-9, only the Incremental algorithm and our algorithm preserve the structure shape and the relative positions of nodes within the structure. **Analysis on The Email-Eu Dataset:** For the email-Eu dataset, which is large in scale and exhibits significant changes in network structure between adjacent timeframes, it is challenging to directly compare and observe layout differences at different timeframes. Figure 11: Layout result comparison based on the Newcomb data. Node 13 and node 8 are highlighted with red and blue circles, their spatial and relative positions are kept stable in our algorithm and the incremental algorithm, but changes in the other two algorithms. Therefore, this paper selected a specific day's network structure with a two-hour time step to showcase the formation process of this structure as the fourth experimental dataset. As shown in Figure 12, the layout results for timeframes 3 to 6 are displayed. From the layout results, the Incremental algorithm present least position changes, but due to certain node positions are overly fixed, we can see the presence of long edges and excessively clustered nodes. In comparison, our algorithm retain the shape and relative positions of some unchanged structures, while also present the overall shape of the network. Based on the layout results on these three datasets, our algorithm achieves a balance between layout stability and quality. It better preserves structural and relative position on significant changes (on time step 4-5 of the first dataset), yet it gives space for reflecting the actual network changes (on the second dataset) and avoiding extreme layout such as too clustered nodes or long edges (on the third dataset).