## 4 Data Analysis  
In Figure 2, the raw data of two gases analyzed are shown. The frequency peaks at 24 h, 12 h, and 8 h, clearly visible in the power spectra, suggest that the temporal fluctuations of the three pollutants are modulated by meteo-climatic cycles (Figure 3). The presence of seasonal components in the time series of CO and O\({}_{3}\) has been reported by [15] in other cities. Before applying the Fisher-Shannon and the Visibility Graph analyses, we removed the cyclic patterns from the time series by applying the following procedure:  
\[Z(t)=\frac{X(t)-\mu(h,d,m)}{\sigma(h,d,m)} \tag{4}\]  
where  
* \(X(t)\) is the original hourly value at time \(t\);
* \(\mu(h,d,m)\) is the mean of the hourly values calculated for the same hour \(h\), day \(d\), and month \(m\) across different years;* \(\sigma(h,d,m)\) is the standard deviation calculated for the same hour \(h\), day \(d\), and month \(m\) across different years;
* \(Z(t)\) is the resulting normalized value. Figure 4 and Figure 5 show, respectively, the normalized time series of \(CO\) and \(O_{3}\) and their spectra. We applied the FS analysis to the normalized series. The two series are characterized by almost identical values of \(N_{X}\) (0.68-0.69) but very different values of FIM (3.65 and 9.68) (Table 1). If the degree of disorder is practically the same for the two series, the degree of organization is the highest for \(CO\) and lowest for \(O_{3}\). Looking at the density of the two  
Figure 4: Normalized hourly time series of (**a**) \(CO\) and (**b**) \(O_{3}\). Figure 5: Power spectrum of the detrended hourly time series of (**a**) \(CO\) and (**b**) \(O_{3}\). Figure 3: Power spectrum of the original hourly time series of (**a**) \(CO\) and (**b**) \(O_{3}\). normalized series (Figure 6), \(CO\) is characterized by multiple peaks that may contribute to the larger FIM. By converting the time series into graphs using the VG method, we calculated the temporal variation of the degree for each series (Figure 7). The degree of a value reflects its capability to be a _lub_ of the series; thus, the larger the degree of a value, the larger its capability to \"attract\" the other values of the series. Table 1 shows, for the two normalized series, the mean degree \(\mu_{k}\), the standard deviation \(\sigma_{k}\), and the coefficient of variation of the degree, defined as follows:  
\[CV_{k}=\frac{\sigma_{k}}{\mu_{k}}. \tag{5}\]  
For \(CO\), all the three parameters are slighlty larger than the corresponding values for \(O_{3}\), indicating that \(CO\) is characterized by more _lub_s than \(O_{3}\). This further suggests a greater complexity in the network generated by the VG for \(CO\) compared to \(O_{3}\), due to the presence of links between values that may be located far apart from each other, if one of them is a _lub_. The larger \(\sigma_{k}\) and \(CV_{k}\) of \(CO\) could also indicate a greater complexity of \(CO\) compared to \(O_{3}\) regarding a more extensive network heterogeneity. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Series** & \(N_{X}\) & **FIM** & \(\mu_{k}\) & \(\sigma_{k}\) & \(CV_{k}\) \\ \hline \(CO\) & 0.68 & 9.68 & 9.67 & 7.87 & 0.81 \\ \(O_{3}\) & 0.69 & 3.65 & 8.29 & 6.19 & 0.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Informational and topological parameters for the analyzed normalized series  
Figure 6: Distribution of the normalized time series of \(CO\) and \(O_{3}\). To identify potential patterns related to the COVID-19 lockdown, we analyzed the temporal variations in \(N_{X}\) (Figure 8a), FIM (Figure 8b), and the coefficient of variation in the degree of the network constructed from the time series using the VG method (Figure 8c). By shifting a 6-month time window over the series in 5-day steps, we calculated these three parameters within each moving window, associating the resulting values with the ending time of the window. This choice balances the need for statistical robustness with the ability to resolve temporal changes in the series.