## 3 Analysis Results
### Structural Variability of Networks  
To investigate the variability in the structure of internal tide networks, we utilized the concept of structural entropy [42], which is based on the community structure within a network. The connection between modularity and structural entropy is presented in Figure 13; a high level of modularity signifies a robust community structure within a network. For SIT networks (Figure 13A), there is no discernible pattern in either structural entropy or modularity for horizontal domains (inner and outer centers). However, for vertical domains (upper and lower layers), a clear differentiation in structural entropy is evident. A little difference in structural entropy for both layers suggests that SITs are weakly influenced by the surface-intensified mesoscale eddy in the upper layer.  
Contrary to SIT networks, DIT networks exhibit distinct patterns in both structural entropy and modularity (Figure 13B): (1) they display high modularity in the inner center and low modularity in the outer center, (2) the upper layer exhibits a higher structural entropy compared to the lower layer, and (3) there is a significant contrast in structural entropy within the inner center for both layers. These findings appear to clarify two aspects: (1) DITs are profoundly influenced by the eddy in the inner center of the upper layer, and (2) DITs exhibit sensitivity to their position within a mesoscale eddy (indicated by colored circles in Figure 13B).  
Time in our data corresponds to the horizontal position within a mesoscale eddy (Figure 2) as the eddy slowly migrates during the glider's virtual mooring observations. Therefore, we examine the temporal evolution of the structural entropy of internal tide networks to understand the structural variability of these networks. The whole-depth networks of both SIT and DIT (Figure 14A) exhibit a growing trend (with the exception of Day 9 in SIT networks), suggesting that the community structure within both networks becomes more random in the outer center compared to the inner center. This behavior is well contrasted with our previous findings, where DITs seem to be more influenced by the  
Figure 13: A composite map of structural entropy and modularity for SIT networks (**A**) and DIT networks (**B**).  
eddy in the inner center than in the outer center. This result implies that the concept of structural entropy should be employed with caution; as stated in [PERSON] and [PERSON] [42], social networks based on certain social factors and brain networks based on anatomy could be inappropriate for this approach. The full-depth SIT and DIT networks seem to belong to those networks from the perspective of geometricity, similar to anatomy in the brain system.  
When we apply the structural entropy methodology separately to the upper and lower layers (Figure 14B), the structural entropy is noticeably high in the upper layer. This indicates that the upper layer is influenced by the surface-intensified eddy. Moreover, for DIT networks, the horizontal domains are clearly distinguished, implying that DIIs in the inner center are strongly modulated by the eddy compared to those in the outer center (green square in Figure 14B). This position-dependent behavior of DITs within the eddy is consistent with the results of our previous analyses.