5.2.1. The Evolution of the Cryptocurrency Network According to Timescales

Figures 3–5 show the results of network structures along with detected communities using the Louvain method with each figure representing a different time window. For each window, four network structures corresponding to four different levels of granularity are displayed. One obvious statement that can be made from the illustrations is that the community structures at each level of granularity change over time. Additionally, if we consider different levels of granularity at the same time, the number of detected communities tends to decrease when the timescale becomes more coarse-grained. For large timescales, such as 24 h, cryptocurrencies build up big groups with few cryptocurrencies acting as central nodes that link directly to the remainder. For example, in Figure 3d, MANA acts as a central node that links all other cryptocurrencies together. This explains why community detection techniques cannot distinguish several subsets as the network in this case is naturally one group. Figure 4d shows a similar pattern, while in Figure 5d there are two central nodes that create two big groups with relatively similar sizes. To this end, with low-frequency data, we expect we can predict the long-term trend of cryptocurrencies in the future by looking at the central nodes from their corresponding community structures. If this is the case, it will be very beneficial for investors who choose a long-term investment. However, this behaviour requires deeper investigation and will be the subject of further research.

(**a**) Time window 1, 30 min (**b**) Time window 1, 6 h

(**c**) Time window 1, 12 h (**d**) Time window 1, 24 h

**Figure 3.** Network structure for the first time window, community detection is applied using Louvain method. Four different timescales are used, e.g., (**a**) 30 min, (**b**) 6 h, (**c**) 12 h, (**d**) 24 h.

We notice that the difficulty of detecting communities in this market increases with the timescale length. In other words, cryptocurrencies are more likely to belong to the same community if we just look at their price values at a high level of granularity such as daily. Thankfully, it can be explained based on the nature of the cryptocurrency market. In particular, the cryptocurrency market is well-known for its high volatility compared to

other traditional asset classes such as stocks, bonds and commodities [113–116]. In [117], the authors used 5 min data of Bitcoin prices traded on three different exchanges, Kraken, Bitstamp and Btcbox, during the period between 2017 and 2021 to calculate the realized volatility (the assessment of variation in returns for an asset by analyzing its historical returns within a defined time period) of this most stable and popular cryptocurrency. The results showed that although Bitcoin is the most valuable and trustworthy cryptocurrency, its volatility fluctuates from 4.8 to 7.5. By contrast, with the same level of granularity, the stock market seems to be more stable, as the realized volatility stood at roughly 0.58 during normal times [118] and increased to just around 1.0 during the COVID-19 pandemic [119]. These facts suggest that the cryptocurrency price fluctuations are dramatic even within a 5 min period. Consequently, using a low-frequency dataset such as 12 h or 24 h appears to cause a loss of important information that influences the results of analysis. This problem has also been described in earlier studies such as [12]. However, existing studies mainly focused on daily data to detect communities in the cryptocurrency market.

(**a**) Time window 2, 30 min (**b**) Time window 2, 6 h

(**c**) Time window 2, 12 h (**d**) Time window 2, 24 h

**Figure 4.** Network structure for the second time window, community detection is applied using Louvain method. Four different timescales are used, e.g., (**a**) 30 min, (**b**) 6 h, (**c**) 12 h, (**d**) 24 h.

In this study, the loss of information by using large timescales including 6 h, 12 h and 24 h makes judging the correlation between different cryptocurrencies unclear. As a result, it affects the corresponding MST which can be seen in Figures 3–5. Ideally, we would like to use a dataset that is as fine-grained as possible. Unfortunately, our experiments show that for frequencies lower than 30 min, there are a huge amount of missing values as some cryptocurrencies are not traded frequently [120], thus requiring their removal or imputing a value. This adversely affects the correlation between time series and impacts our analysis. Finally, we choose a 30 min dataset for further experiments.

(**a**) Time window 3, 30 min (**b**) Time window 3, 6 h

(**c**) Time window 3, 12 h (**d**) Time window 3, 24 h

**Figure 5.** Network structure for the third time window, community detection is applied using Louvain method. Four different timescales are used, e.g., (**a**) 30 min, (**b**) 6 h, (**c**) 12 h, (**d**) 24 h.

5.2.2. Louvain vs. Girvan–Newman for Community Structure Detection

The Louvain method is our main technique for detecting communities but we also use the Girvan–Newman method to double-check the communities found. The *v*-*measure* gives the similarity between these two methods [121], shown in Table 5. This metric ranges from 0 to 1 such that 0 indicates a complete dissimilarity between two graphs while 1 indicates a complete similarity. We found that the *v-measure* in all cases is high with the lowest value of 0.82 from the third time window in the 6 h dataset in Table 5. That is, the Louvain method proposes similar results as Girvan–Newman. Thus, the communities found by Louvain are reliable for use in further analysis.


**Table 5.** *v-Measure* between Louvain and Girvan–Newman methods.

*5.3. Analysis of Investors' Investment Decisions Based on the Time-Varying Network Structure* 5.3.1. The Changes in Crypto Network Structure during Times of Crisis

To observe the growth of the network structure over time, we use *Degree Assortativity Coefficient* [122] and *Average Betweenness Centrality* [3]. However, these metrics fail to tell us the similarity between two networks. Thus, to statistically compare the topological change between two networks, we use three more metrics, including *v-measure*, *Degree centrality* [26] and *Eigenvalue method* [123,124].

Table 6 shows results of *Betweenness Centrality* and *Degree Assortativity*. Immediately, we can see that there is a huge change occurring in time window 2, which corresponds to the turbulent time caused by the pandemic on both metrics.

Regarding the *Betweenness Centrality*, this metric decreases from 0.15 in time window 1 to 0.05 in the next period before going back to its original value prior to the pandemic outbreak (time window 1). A reasonable explanation for this movement is that the network structure of the cryptocurency market during normal times appears to have a dispersive tendency with the whole network divided into multiple small-size groups such that each group share common characteristics. However, during COVID-19, these synchronize to form a big group. Thus, the number of groups decreases while the size of each group increases. This might be a consequence of an increase in the connectedness of cryptocurrencies during the pandemic, as shown in many research papers [11,27,45]. In the recovery time, however, the network started to divide into smaller parts again, perhaps because the cryptocurrency market overcame the most connected period and started to go back to its normal behavior.

The *Degree Assortativity* results strongly support those of the *Betweenness Centrality*. In particular, a negative value shows that high-degree nodes are more likely to link to lowdegree nodes, which means that each group in the network has one node acting as a central node connecting to the rest. While the values in time window 1 and 3 are approximately the same, time window 2 shows a decline by nearly 50 percent. This indicates that the number of connections between high-degree nodes and low-degree nodes increases, i.e., the network forms big groups with a large number of leaf nodes in each group.

We notice that this time-varying structure is similar to what have been shown in works of Drozdz et al. [20,21], who stated that the market has a distributed-network topology or a hierarchical-network topology in which no node dominates the network during normal times. However, it becomes more centralized during the pandemic and started to distribute as this turbulent time is gone. More recently, another work proposed by Nie also confirmed the same result [22].

Table 7 shows results of the three similarity metrics for different time periods: *normal time* (time window 1), *downtime* (time window 2) and *recovery time* (time window 3). Each values shows the similarity between two time windows. For *v-measure*, the higher the value is, the more alike two networks are. On the other hand, for the remaining values, a lower value indicates that two networks are more similar.

The differences between time window 2 and the other two time windows are very clear. In particular, the *v-measure* between time window 1 and 3 is 0.32, meaning that communities found in time window 3 hold roughly one third of characteristics from time window 1's communities. By contrast, *v-measure* values between time window 1 and 2 as well as between time window 2 and 3 are negligible, standing at 0.04 and 0.02, respectively. Additionally, for the topological structures of MSTs, the other two metrics also show the same principle since time window 1 and 3 share common characteristics and the similarity degree of other cases are nearly zero. Remarkably, the *Eigenvalue method* shows a significant divergence of time window 2 with others, as shown in Table 7.

The severe pandemic and the global downturn of March 2020 together seem to have actually changed the way cryptocurrencies interact with each other. The changes of these interactions have created new communities and broken down old ones, i.e., some cryptocurrencies become closer to each other while others moved further away from each other due to the COVID-19 pandemic and the economic recession. Eventually, the topological structure during this turbulent time shows completely different patterns compared to the periods when the global market is stable. Furthermore, we noticed that the community structure started to recover back to its pre-COVID-19 levels after June 2020, which coincides with the time the global economy recovered and the COVID-19 pandemic had less impact. During this time, some characteristics of the network structure reappeared that are similar to the structure during the normal time (it is obvious that these structures are not fully similar because they change over time, as proven in previous sections and, in addition, after June 2020, the global economy started to recover, but not as well as in the past, and the pandemic still had an impact on the economy worldwide to some extent). This is why the *v-measure* between time window 1 and 3 increased significantly and the corresponding differences measured by *Degree centrality* and *Eigenvalue method* are very small. The community structures for the three time windows are shown in Figures 3a, 4a and 5a.

**Table 6.** The growth of network structures over time measured by Betweenness Centrality and Degree Assortativity.


**Table 7.** Similarity in network structures between different phases of the cryptocurrency market measured by three metrics. A higher value of *v-measure* indicates a greater similarity between two structures, whereas, higher values of *degree centrality* and *eigenvalue method* indicate more dissimilarity between two structures.


5.3.2. Learning the Investment Decision of Crypto Traders Based on Ranking Distribution

The ranking of a cryptocurrency is measured by its market capitalization (a multiplication between the number of coins in circulation and the current market price of a single coin). We obtain cryptocurrencies' ranking on the https://coinmarketcap.com website (accessed on 15 August 2022).

We use this characteristic of cryptocurrencies to examine how they are distributed in each community of the cryptocurrency network. More importantly, we will have a look at the way cryptocurrencies form groups during different phases of the global economy by observing the distribution of ranking in each group between different periods of time.

Table 8 summarizes the results of community detection using the Louvain method. For each period of time, the found communities are listed with a set of cryptocurrencies and corresponding rankings belonging to each of them. We found that during the normal time, there is a mix between high-ranking and low-ranking cryptocurrencies in each community. For example, group 6 has a size of 7 including top-ranking cryptocurrencies such as BTC, ETH and BCH, while also having very low-ranking ones such as MAID and ICX. We pay more attention to communities found in the downturn time. At this phase, we recognized that the community formation of these cryptocurrencies seems to be dramatically different from the previous period. In particular, there are only two communities found during this period, while the other has six. More importantly, there seems to be a separation between high-ranking and low-ranking cryptocurrencies, because the majority of top-ranking cryptocurrencies belong to one group while the majority of low-ranking cryptocurrencies are in the other. Additionally, by comparing these results with the period of recovery, we noticed that this period shares common characteristics with both normal time and downturn time. Specifically, after the downturn time, cryptocurrencies started to separate from each other; this can be seen by looking at the number of communities during this time. There was an increase from 2 to 6, which is equal to the normal time case. While the majority of communities show a mix between high- and low-ranking cryptocurrencies, there are two communities that are similar to the downturn time: group 4 with all high-ranking cryptocurrencies and group 5 with all low-ranking cryptocurrencies.


**Table 8.** Distributions of rankings in each community during different phases of the financial market: normal time, downturn time and recovery time. The rankings are sorted in ascending order. Bold values are minimum and maximum ranks in each period.

Figure 6 shows the distribution of cryptocurrencies' rankings in three different phases of time. We use this visualization to show readers the changes of ranking distributions in a clearer and easier manner. Each community is represented by a circular shape while the rankings of cryptocurrencies are represented by the intensity of the blue color, i.e., the darker the blue, the lower the cryptocurrency's rank. Figure 6b shows that the circular shape of group 1 is clearly darker than that of group 2. On the other hand, there is a combination of both bright and dark blue in the majority of cases in two remaining sub-figures. Notably, Groups 3 and 5 in Figure 6c show a clear difference from the rest.

When it comes to these results, investors' investment decisions can be considered as potential explanations for the time-varying community structure. During normal times, i.e., when the financial market is stable and there is no major event occurring that impacts wider society, investors show a non-herding behaviour. That is, their decision for investing in a cryptocurrency is based on their own market analysis and is not influenced by other investors' choice. This might push up the vibrancy of the cryptocurrency market where a large number of coins with both high and low rankings are traded. As a result, there is a diversification in terms of rankings in each community. Empirically, it is found that there was no herding behavior before the pandemic. In particular, Larisa et al. in [125] used hourly price time series of multiple exchanges such as Binance, Bitbay, BitFinex, Coinbase and major cryptocurrencies including BTC, LTC and ETH to find the existence of herding before the start of COVID-19. Based on the *Cross Sectional Absolute Deviation* model, they found that the herding behavior was free during this time. By contrast, during a turbulent time, investors are panicked by the fluctuations of cryptocurrencies' price as well as being bombarded by bad news that strongly affect their investment. Different studies have been carried out to investigate the investors' behavior since the onset of the COVID-19 outbreak. Generally speaking, these reached the same conclusions: that the pandemic actually increased herding behavior in the cryptocurrency market. In [126], the authors used 43 cryptocurrencies with large market capitalization between 2013 and 2020; they

found that investors in the cryptocurrency market follow the consensus and the impact of coronavirus media coverage is significant on the herding behavior. In particular, news related to the coronavirus increases fear and affects the behavior of investors reducing appetite for risk. Consequently, investors disregard their private information and follow others' investment decisions. However, the impact of media is reduced when the market returns to a normal phase. This is in line with different studies that use different datasets and time periods [125,127,128]. More importantly, the way investors show herding behavior is that they tended to invest in the major and most-tradable cryptocurrencies [27]. This can be explained by the fact that high-ranking cryptocurrencies are more mature so they are more stable than the rest and are more likely to retain value under the uncertainty of the global financial market, causing a bias from investors [129]. Consequently, major cryptocurrencies were seen to increase in terms of trading volume and act as a store of value during the turbulence times [130]. In other words, there was a risk aversion occurring after the pandemic outburst as described in [72]. Eventually, all high-ranking cryptocurrencies belonged to one group.
