## 3 Analysis Results
### Characteristics of Minimal Spanning Tree (MST)  
To examine the variability of coherence structures of internal tides, we employ the total weights of MST networks to detect the distinguishing behavior in the sub-domains of the studied eddy. MST networks are established via [PERSON]'s algorithm using distance matrices based on wavelet-coherence matrices for SIT and DIT signals, respectively. Thus, it should be noted that MST networks are different from the SIT and DIT networks because the MST networks are not subject to thresholding. The total weights of MST evaluate the degree of overall coherence of the wavelet-coherence matrix constructed from internal tides, with low values representing strong coherence and high values indicating incoherence. Since this value depends on the network's size (number of nodes), we can make only qualitative evaluations via relative comparison.  
For SITs, our analysis revealed that the lower layer is more coherent than the upper layer (Figure 11B,C), but the structural distinction between the inner (Day 1 through Day 5) and outer centers (Day 6 through Day 9) is not clear, as there is no distinctive variation pattern of MST weights between those horizontal domains.  
In contrast, for DITs, a distinct variability in MST weights in the upper layer is clearly observed (Figure 12B), with a high weight in the inner center and a low weight in the outer center, consistent with previous analysis results (Figure 10). It is important to note that all of these results are statistically significant compared to those of the wavelet-based surrogate dataset (see the dotted error bar in Figures 11 and 12).  
It should be noted that the numerical values of MST weights for DITs are generally lower than those of SITs (as shown in Figures 11 and 12); this difference could be caused by other factors rather than interactions. In [PERSON]'s study [44], it was found that SITs in the study area originated from multiple formation sites, while DITs mainly originated from the Luzon Strait. Therefore, it is important to take into consideration the multiplicity of internal  
Figure 10: Same as Figure 9 except for DIT (Diurnal Internal Tide) networks. A chart of mean clustering coefficients (**A**) and a composite map of mean degree and mean clustering coefficient (**B**) for DIT (Diurnal Internal Tide) networks.  
According to the definition of MST, low coherences among nodes result in a high MST total weight and vice versa. Thus, the overall exceeding trend of SIT over DIT, with no temporal trend (position-dependent pattern), implies that SIT's incoherent behaviors are mainly due to the multiplicity of SITs at the study site rather than interactions between SITs and the eddy. If significant interactions existed between SITs and the eddy, a position-dependent pattern should be observed in the upper and lower layers, which is not the case (Figure 11). As for DITs, the pattern of total weights of MST in the upper layer is distinctive: the value is high in the inner center and low in the outer center (Figure 12B). These findings could be evidence of strong interactions between DITs and the eddy in the inner center of the upper layer and the horizontal inhomogeneity of a surface-intensified mesoscale eddy.