## 3 Analysis Results
### Spatial Pattern of Degree Distribution of IMF Networks  
From degree (connectivity) spatial patterns of IMF networks (Figures 9-13), we first detect the hub-region where densely connected nodes form a cluster. As shown in Figure 9, the low-mode IMF networks (IMF-2 through IMF-5) have a hub-spot in the northern part of the EJS, near the ESIW formation site. However, in the high-mode IMF networks (IMF-6 through IMF-8), the hub-spots suddenly appear in the southern area of the EJS near the coastal area of Japan and extend from the Japan coast towards the interior with increasing  
Figure 8: Temporal evolution of the instantaneous energy density level (IE) with respect to the IMF.  
mode numbers. Since the level of PCC indicates the degree of synchrony of a pair of oscillatory signals like in this study, any atmospheric forcing with a shorter timescale seems to be dominant in the northern part of the EJS, while any advective forcing with a longer timescale seems to play a significant role in the southern EJS; note that most flowing-in waters enter through the KTS.  
The seasonality in the topology of IMF networks is clearly observed for the monthly to semiannual time scales (IMF-3 through IMF-5 in Figures 11 and 13) in the summer and winter seasons, as confirmed in the IE spatial patterns. The difference is the way of partitioning the EJS; in the IE distribution, the EJS is divided into the north-western and north-eastern parts (Figures 5 and 7), while in a degree distribution, the EJS is divided into the north and south parts (Figures 11 and 13). This different space-dividing behavior is fundamentally attributed to the magnitude and the spatial range of any forcing, respectively. The IE level is directly connected to the magnitude of forcing, while the level of degree or connectivity (based on the level of PCC values) is deeply related to the fluctuating behavior (relating to phase difference or lag time).  
A noticeable thing is that there is a clear contrast between the spatial extents of PCC among nodes in the north and south of the EJS. There could be a substantial effect of a persistent gyre on the correlation structure in the northern EJS (Figure 1). It should be noted that the persistent hub-spot observed in low-mode IMFs (IMF-2 through IMF-5 in Figure 9) resides in the interior of the gyre.  
In addition, the connectivity structure of all IMF networks is explored via assortativity. As shown in Figure 14, all networks are assortative, that is, hubs tend to make a greater cluster; this behavior is seen in Figures 9-13. Figure 14 shows the varying level of assortativity of all IMF networks with respect to mode number; irrespective of seasons, there appears to be a similar behavior of a high value for low-mode IMF networks and a low value for high-mode ones, except for IMF-9 and IMF-10. This persistently positive assortativity in all IMF networks (Figure 14) gives some clues on the spatiotemporal extents of any forcing; forcing with smaller timescales tends to have a narrow spatial coverage, while forcing with larger timescales has a wide spatial coverage. This behavioral feature  
Figure 9: Spatial pattern of degree distribution of IMF networks, constructed from the database with the full length of observation from September 1981 to April 2023.  
Figure 12: The same as Figure 9, except for autumn (SON).  
Figure 13: The same as Figure 9, except for winter (DJF).