*4.5. Time Window Division*

Given the dataset described earlier, one important question about constructing a network structure in these cryptocurrencies is how to split the dataset into different consecutive periods. This is because a network structure corresponding to each period of time should be able to explain what has happened to the cryptocurrencies throughout that time, i.e., there must be a reason behind this topological structure. If we divided the dataset

randomly, we could not capture important historical events at a specific period. As a result, the topology we found would be meaningless in the corresponding time window. To this end, we must select time windows rationally. We note that our dataset contains the period of the COVID-19 pandemic as well as the global downturn 2020. From the literature in Section 2, we see these historical events actually adversely influenced the financial markets. Thus, we postulate that the COVID-19 pandemic is a reasonable milestone to separate our dataset.

To verify the pandemic's impact on the global economy and thereby choose the right time windows for the dataset, we consider the movements of four different factors. Firstly, the attention to the COVID-19 pandemic, as measured by the frequency of COVID-19-related keywords searched on Google Trends. For this factor, we use two keywords including *COVID-19* and *coronavirus disease 19* . Secondly, we use the VIX index to observe fluctuations of the stock market, this index starts at 0 for no upper bound and a higher value implies that the stock market has stronger fluctuation. Thirdly, we also observe the prices of the *S*&*P*500 index, representing the US economy. Lastly, the growth rate of the world's GDP is used as a proxy for the development of the global economy in general.

Figure 1 visualizes these aforementioned factors. From Figure 1a, people started to worry about this disease in January 2020. However, it was not until March 2020 that the COVID-19 pandemic actually caught the attention of people worldwide, as the volume of searches for COVID-19-related terms quickly peaked. This remained a topic of interest until July 2020. Furthermore, March 2020 was the month in which a pandemic-induced economic recession first occurred, seriously affecting the economy of nations worldwide. This effect is shown in Figure 1b–d. In particular, the GDP's growth rate decreased by 3.3% in 2020, which is the highest decrease ever, even worse than the Great Recession in 2007–2009 [110]. Simultaneously, the stock market fluctuated dramatically, which can be seen via the VIX index and the *S*&*P*500 index, both of which experienced a significant fall during March 2020. However, the economy started to recover afterward, the stock market became less fluctuated and the *S*&*P*500 index regained its original pre-pandemic value in July 2020.

**Figure 1.** The reaction of general public and global economy to the COVID-19 pandemic. Four factors are considered: (**a**) Worldwide attention to the pandemic, (**b**) Global GDP growth, (**c**) VIX index, (**d**) *S*&*P*500 index.

Consequently, we split the 784 days from 13 February 2019 to 6 April 2021 into three time windows which correspond to three different stages, including normal time, downturn time and recovery time. The details for these time windows are shown in Table 3.

**Table 3.** Three time windows used in this work (time windows split to take into consideration the COVID-19 pandemic).

