## 4 Data Analysis
Each 6-month window contains approximately 4,320 data points, ensuring a sufficiently large sample size for reliable estimation of the probability density function, on which the FS method is based, and for the calculation of the coefficient of variation of the degree of the visibility network. A larger dataset within each window leads to a more accurate characterization of the signal's statistical features. Moreover, the 6-month length allows for an adequate number of windows to be positioned before the onset of the COVID-19 pandemic, making it possible to observe and compare the behavior of the FS and VG complexity in both the pre-COVID and COVID-affected periods. Using substantially longer windows would have reduced the resolution in the pre-COVID phase, hindering the detection of the changes that emerged during the pandemic. Figure 7: Time distribution of the degree \(k\) of (**a**) \(CO\) and (**b**) \(O_{3}\). Figure 8: Time variation in (**a**) \(N_{X}\), (**b**) FIM, and (**c**) \(CV_{k}\). In all cases, we observe that during the COVID-19 lockdown, approximately between April and September 2020, the three parameters show a clear difference between _CO_ and _O_\({}_{3}\). In particular, for _CO_, _N_\({}_{X}\) decreases, while FIM and _CV_\({}_{k}\) increase. During lockdown, the three parameters for _O_\({}_{3}\) remain almost stationary and do not exhibit any significant anomalous trends. After lockdown, the three parameters for _CO_ and _O_\({}_{3}\) tend to align with each other, indicating a clear correlation. The combined FS and VG analyses reveal that the temporal behavior of CO is shaped by more localized and intermittent emissions, leading to high structural complexity and organization. _O_\({}_{3}\), by contrast, reflects broader-scale chemical processes and environmental modulation, resulting in smoother, less structured variability. These insights help to bridge the gap between pollutant emission mechanisms and their statistical representation, offering a valuable perspective for interpreting air quality time series. While the combined use of the FS and VG methods has enabled us to uncover complex patterns and meaningful structural differences between _CO_ and _O_\({}_{3}\), it is important to acknowledge certain inherent limitations of the analysis. The use of a 6-month moving window provided a good balance between statistical robustness and temporal resolution; however, this approach may smooth out very short-term events or abrupt changes. Additionally, although the visibility graph technique effectively captures structural properties of time series, it can be sensitive to outliers or noise, potentially affecting metrics such as hub identification or degree heterogeneity. On the other hand, while the data used are of high quality and resolution, they may not fully reflect the spatial variability of emission sources or local meteorological influences. Finally, although a clear signal was identified during the COVID-19 lockdown period, it is possible that other concurrent factors--such as seasonal effects or regional atmospheric processes--also contributed to the observed patterns. Nevertheless, the results provide a solid foundation for advancing the understanding of the temporal dynamics of urban pollutants and exploring new approaches for air quality time series analysis.