## 2 Materials and Methods
### Earthquake Networks Based on Similar Activity Patterns  
[PERSON] et al. [60] suggested the construction of the ENBOSAP as follows: The area under study was evenly spaced in geographical coordinates in \"squares\" of dimensions of about 100 km \(\times\) 100 km, each marked by two integers \((i,j)\). The center of each \"square\" is a possible node of the network. The fact that EQs do not occur on a daily basis in every square makes it necessary to coarse-grain the seismic activity over a predefined time interval. There is a trade-off between precision and data richness leading [60] to an optimal coarseness in the 90-day time series. Thus, the seismic activity \(s_{t}\) in each square covered 90 days and \(s_{t+1}\) corresponded to the next 90 days of non-intersecting time periods, giving about 4 different values per year. The energy released in each 90-day period inside the \"square\" with indices \((i,j)\) was given by [60]:  
\[s_{t}(i,j)\equiv\sum_{l=1}^{N_{t}(i,j)}10^{\frac{3}{2}\text{M}_{t}^{l}(i,j)}, \tag{4}\]  
where \(N_{t}(i,j)\) is the number of EQs displayed in the 90-day \(t\)-th time window with epicenter inside the square \((i,j)\) of magnitude \(\text{M}_{t}^{l}(i,j)\) above a given threshold \(\text{M}_{\text{\emph{thres}}}\), i.e., \(\text{M}_{t}^{l}(i,j)\geq\text{M}_{\text{\emph{thres}}}\). To define a link between the centers of two squares, say \((i,j)\) and \((i^{\prime},j^{\prime})\), one calculated the Pearson product-moment correlation \(r_{x,y}\) between the time series \(x_{t}\equiv s_{t}(i,j)\) and \(y_{t}\equiv s_{t}(i^{\prime},j^{\prime})\):  
Figure 2: Results for the variabilities \(\beta_{\text{W}}\) when \(W=80\) and 120 consecutive EQs of the seismicity order parameter \(\kappa_{1}\) in natural time for the almost 40-year study period with the marginal geographical areas \(A_{6}\) and \(A_{5}\) that enclose the 6-core and the 5-core of the ENBOSAP of the region \(\text{N}_{22}^{50}\text{E}_{5}^{46}\), respectively. The magnitude of EQs (right scale) is depicted by the (black) vertical lines ending in solid circles for EQs that occur within the \(A_{6}\). When the vertical line does not end in a solid circle, the EQ occurs inside the \(A_{5}\), but outside the \(A_{6}\), i.e, the 2017 M7.3 Halabja EQ. The (red) open circles indicate the uniquely identified minima \(\beta_{120}\)[115] when comparing the \(\beta_{\text{W}}\) values for both areas \(A_{6}\) and \(A_{5}\). They precede all the mainshocks of \(M\geq 7.1\) within \(A_{6}\) by six months at the most, without false alarms, see the red rectangle of Figure 1. The horizontal line at 0.253 was designed as an eye guide.  
\[r_{x,y}\equiv\frac{\langle xy\rangle-\langle x\rangle\langle y\rangle}{\sigma_{x} \sigma_{y}}, \tag{5}\]  
where \(\langle\ldots\rangle\) indicates the average value of \(\ldots\), and \(\sigma_{x}\) and \(\sigma_{y}\) are the standard deviations of \(x_{t}\) and \(y_{t}\), respectively. The two grid squares were linked if \(r_{x,y}\) was greater than a specified value \(r_{c}\), which is a tunable parameter. [PERSON] and [PERSON] [115] found that, for NTA applications of ENBOSAP, \(r_{c}\) should be chosen as the one that determines the upper 5% percentile of the positive \(r_{x,y}\) among all the different squares; for the eastern Mediterranean region, the value \(r_{c}=0.7\) was selected. As usual, the degree \(k\) of a node was the number of links the node had. [PERSON] et al. [60] showed that ENBOSAP: (a) displays links without a characteristic length scale with much more links than expected only by chance alone, (b) is much more assortative than random ones, and (c) exhibits significant stability over time. These findings corroborated the existence of high-degree nodes with similar activity patterns over a distance of more than 1000 km away; see, for example, Figure 1.