# Cryptocurrency Market Consolidation in 2020–2021

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Results and Discussion

- (1)
- Exactly as expected from the above discussion related to Figure 5, for each data type, the degree of the most connected nodes tends to decrease with increasing s and the degree gap between ${k}_{\mathrm{max}}$ and the smaller values of ${k}_{i}$ decreases as well. For longer time scales, the topology becomes less centralized and more “democratic” with a few hubs of a comparable connectivity.
- (2)
- As the most capitalized cryptocurrency, BTC remains the most connected node over the longest time for $s=10$ min and, to a lesser extent, for $s=60$ min. However, for $s=360$ min, it ceases to play such a role in August 2020, when the MST becomes decentralized permanently and the most connected node can be a cryptocurrency of moderate capitalization (see, for example, [73] for a similar observation).
- (3)
- It happened for $s=10$ min that the periods when ETH was the most connected node as frequently as BTC prevailed between September 2020 and February 2021. For $s=60$ min also some other assets like ONT and TRX are represented by the most connected nodes from time to time, but it happens more because of a temporarily diminished degree of BTC and ETH than because of their own importance.
- (4)
- In the residual data, BTC does not play so substantial role as in the original data, because its dominating role was largely wiped out by filtering out the ${\lambda}_{1}$ contribution. It remains, however, a hub with the second largest connectivity throughout the whole analyzed interval for $s=10$ min. If s is increased to 60 min, BTC is degraded further on to be among a few secondary hubs with a few connections only. For both the scales, the most connected node is FTT, but its distinguished structural position vanishes almost completely after April 2021. For $s=360$ min the MSTs always show a decentralized topology.
- (5)
- If the prices are expressed in BTC, ${k}_{\mathrm{max}}\left(t\right)$ is typically smaller (${k}_{\mathrm{max}}<30$ out of 68) than when they are expressed in USDT (${k}_{\mathrm{max}}<70$ out of 80). This is the expected property as BTC is the most connected hub in the case of the prices given in a stable coin. For any scale, a typical situation in this case is that there is frequent alternation of the most connected nodes: ETH, BNB, LINK, ONT, LTC, XRP, DASH, and so forth are among the assets that have the largest degree in certain time intervals, but none of them is able to substantially centralize the network. For long time scales, it even occurs that the largest degree nodes are switched almost random.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Dukascopy | Binance | ||||
---|---|---|---|---|---|

Ticker | Name | Ticker | Name | Ticker | Name |

BTC | bitcoin | BTC | bitcoin | LINK | chainlink |

ETH | ethereum | ADA | cardano | LTC | litecoin |

DASH | dash | ALGO | algorand | MATIC | polygon |

EOS | eos | ANKR | ankr | MFT | hifi finance |

XMR | monero | ARPA | arpa chain | MITH | mithril |

AUD | Australian dollar | ATOM | cosmos | MTL | metal |

EUR | euro | BAND | band protocol | NANO | nano |

GBP | British pound | BAT | basic atention token | NEO | neo |

NZD | New Zealand dollar | BCH | bitcoin cash | NKN | nkn |

CAD | Canadian dollar | BEAM | beam | NULS | nuls |

CHF | Swiss franc | BNB | binance coin | OMG | omg network |

CNH | offshore renminbi | BTT | bittorrent | ONE | harmony |

CZK | Czech krone | BUSD | binance USD | ONG | ontology gas |

JPY | Japanese yen | CELR | celer network | ONT | ontology |

MXN | Mexican peso | CHZ | chiliz | PAX | pax dollar |

NOK | Norwegian krone | COS | contentos | PERL | perl |

PLN | Polish zloty | CTXC | cortex | QTUM | qtum |

ZAR | South African rand | CVC | civic | REN | ren |

NIKKEI | Nikkei 225 | DASH | dash | RLC | iexec |

RUSSEL | Russell 2000 | DENT | dent | RVN | ravencoin |

DAX | DAX 30 | DOCK | dock | STX | stacks |

FTSE | FTSE 100 | DOGE | dogecoin | TFUEL | theta fuel |

DJI | Dow Jones Industrial Average | DUSK | dusk network | THETA | theta |

SP | S&P 500 | ENJ | enj coin | TOMO | tomochain |

NQ | NASDAQ 100 | EOS | eos | TROY | troy |

XAG | silver | ETC | ethereum classic | TRX | tron |

XAU | gold | ETH | ethereum | TUSD | trueusd |

HG | high-grade copper | FET | fetch | USDC | USD coin |

CL | crude oil | FTM | fantom | VET | vechain |

FTT | ftx token | VITE | vite | ||

FUN | funtoken | WAN | wanchain | ||

GTO | gifto | WAVES | waves | ||

HBAR | hedera | WIN | winklink | ||

HOT | holo | XLM | stellar | ||

ICX | icon | XMR | ripple | ||

IOST | iost | XRP | monero | ||

IOTA | miota | XTZ | tezos | ||

IOTX | iotex | ZEC | zcash | ||

KAVA | kava | ZIL | zilliqa | ||

KEY | key | ZRX | 0x |

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**Figure 1.**Price evolution of bitcoin (BTC) expressed in US dollars (black) and the BTC share in the total cryptocurrency market capitalization (magenta) over the period from 1 January 2020 to 31 October 2021. Characteristic events are indicated by vertical dashed lines and Roman numerals: COVID-19 crash in March 2020 (event I), strong bull market on cryptocurrency valuation October 2020–April 2021 (event II), all-time high on 14 April 2021 (event III), the May crash on the cryptocurrency market (event IV), and recent rally with new all-time high on 20 October 2021 (event V).

**Figure 2.**Time evolution of the selected spectral characteristics of the q-dependent detrended correlation matrix ${\mathbf{C}}_{q}\left(s\right)$ for $q=1$ (

**a**) and $q=4$ (

**b**). A moving window of a length of 7 days shifted by 1 day was applied for sample values of the scale: $s=10$ min (red), $s=60$ min (blue), $s=180$ min (green), and $s=360$ min (orange). The largest eigenvalue ${\lambda}_{1}$ (top panels in (

**a**,

**b**)), the Shannon entropy $H\left({\mathbf{v}}_{1}\right)$ of the squared eigenvector components ${v}_{1}\left(j\right)$ with $j=1,...,N$ (middle panels), and the squared maximum component of the eigenvector ${\mathbf{v}}_{1}$ associated with ${\lambda}_{1}$ (bottom panels) are shown. The cryptocurrency prices are expressed in USDT.

**Figure 3.**Time evolution of the selected spectral characteristics of ${\mathbf{C}}_{q}\left(s\right)$ (continuing). As in Figure 2, two cases are shown: $q=1$ (

**a**) and $q=4$ (

**b**). A moving window of length 7 days shifted by 1 day was applied for sample values of the scale: $s=10$ min (red), $s=60$ min (blue), $s=180$ min (green), and $s=360$ min (orange). The second largest eigenvalue ${\lambda}_{2}$ (top panels), the Shannon entropy $H\left({\mathbf{v}}_{2}\right)$ of the squared eigenvector components ${v}_{2}\left(j\right)$ with $j=1,...,N$ (middle panels), and the squared maximum component of the eigenvector ${\mathbf{v}}_{2}$ associated with ${\lambda}_{2}$ (bottom panels) are shown.

**Figure 4.**Time evolution of the selected spectral characteristics of the residual q-dependent detrended correlation matrix ${\mathbf{C}}_{q}^{\left(\mathrm{res}\right)}\left(s\right)$ after filtering out the component corresponding to ${\lambda}_{1}$. As in Figure 2, two cases are shown: $q=1$ (

**a**) and $q=4$ (

**b**). A moving window of length 7 days shifted by 1 day was applied for sample values of the scale: $s=10$ min (red), $s=60$ min (blue), $s=180$ min (green), and $s=360$ min (orange). The largest residual eigenvalue ${\lambda}_{1}^{\left(\mathrm{res}\right)}$ (top panels), the Shannon entropy $H\left({\mathbf{v}}_{1}^{\left(\mathrm{res}\right)}\right)$ of the squared eigenvector components ${v}_{1}^{\left(\mathrm{res}\right)}\left(j\right)$ with $j=1,...,N$ (middle panels), and the squared maximum component of the eigenvector ${\mathbf{v}}_{1}^{\left(\mathrm{res}\right)}$ associated with ${\lambda}_{1}^{\left(\mathrm{res}\right)}$ (bottom panels) are shown.

**Figure 5.**Node degree cumulative distribution $P(X\ge k)$ of the MSTs created for the cryptocurrency prices expressed in USDT. Results for sample moving windows are shown for $q=1$ (

**a**) and $q=4$ (

**b**). In each panel the distributions for two temporal scales are displayed: $s=10$ min (red) and $s=360$ min (blue). The nodes with the highest degree k are labelled by the corresponding cryptocurrency ticker.

**Figure 6.**Evolution of the node degree ${k}_{i}$ for the most connected nodes of the MST calculated in the seven-day-long moving window with a step of 1 day. For the prices expressed in USDT, two cases are shown: (

**a**) the results for the complete data set without any filtering and (

**b**) the results for the residual signals after filtering out a contribution from the component represented by the largest eigenvalue ${\lambda}_{1}$. The results for (

**c**)—the prices expressed in BTC, which corresponds to filtering out any BTC-related contribution to other assets’ evolution, are also shown. In each case, three exemplary scales are shown: $s=10$ min (top graph in each panel), $s=60$ min (middle graph), and $s=360$ min (bottom graph). Different colors and line styles denote the node degree for different cryptocurrencies.

**Figure 7.**Minimal spanning trees calculated from a distance matrix ${\mathbf{D}}_{q}\left(s\right)$ based on ${\rho}_{q}\left(s\right)$ for $q=1$ and $s=10$ min. Each node represents a cryptocurrency and the edge widths are proportional to value of the corresponding coefficient ${\rho}_{q}\left(s\right)$. Each MST was created for moving window of length 7 days ended at specific dates: (

**a**) 6 April 2020, (

**b**) 1 August 2020, (

**c**) 9 October 2020, and (

**d**) 25 February 2021.

**Figure 8.**Minimal spanning trees calculated from a distance matrix ${\mathbf{D}}_{q}\left(s\right)$ based on ${\rho}_{q}\left(s\right)$ for $q=1$ and $s=360$ min. Each node represents a cryptocurrency and the edge widths are proportional to value of the corresponding coefficient ${\rho}_{q}\left(s\right)$. Each MST was created for moving window of a length of 7 days ended at specific dates: (

**a**) 6 April 2020, (

**b**) 1 August 2020, (

**c**) 9 October 2020, and (

**d**) 25 February 2021.

**Figure 9.**Time evolution of the selected network characteristics of the MST created from a distance matrix ${\mathbf{D}}_{q}\left(s\right)$. Two cases are shown: $q=1$ (

**a**) and $q=4$ (

**b**). In each case, a moving window of length 7 days shifted by 1 day was applied for the scales: $s=10$ min (red), $s=60$ min (blue), $s=180$ min (green), and $s=360$ min (orange). The mean path length $\langle L(q,s,t)\rangle $ (top panels), the node degree cumulative probability distribution $P(X\ge k)$ power-law slope exponent $\gamma (q,s,t)$ (middle panels) together with its standard error (SE, bottom panels). The cryptocurrency prices are expressed in USDT.

**Figure 10.**The same quantities as in Figure 9 but here obtained from the residual MSTs calculated for ${\mathbf{D}}_{q}^{\left(\mathrm{res}\right)}\left(s\right)$ after filtering out the component corresponding to ${\lambda}_{1}$. Two cases are shown: $q=1$ (

**a**) and $q=4$ (

**b**). The cryptocurrency prices are expressed in USDT.

**Figure 12.**Composition of the BTC-related cryptocurrency cluster as a function of time for sample temporal scales: $s=10$ min (

**top**), $s=60$ min (

**middle**), and $s=360$ min (

**bottom**). Each point on the horizontal axis represents a non-overlapping seven-day-long moving window. Asset prices have been expressed in USDT.

**Figure 13.**Composition of the ETH-related cryptocurrency cluster as a function of time for sample temporal scales: $s=10$ min (

**top**), $s=60$ min (

**middle**), and $s=360$ min (

**bottom**). Each point on the horizontal axis represents a non-overlapping seven-day-long moving window. Asset prices have been expressed in BTC, therefore any BTC-related contribution has been filtered out.

**Figure 14.**Composition of the BNB-related cryptocurrency cluster as a function of time for sample temporal scales: $s=10$ min (

**top**), $s=60$ min (

**middle**), and $s=360$ min (

**bottom**). Each point on the horizontal axis represents a non-overlapping seven-day-long moving window. Asset prices have been expressed in BTC, therefore any BTC-related contribution has been filtered out.

**Figure 15.**Composition of the ONT-related cryptocurrency cluster as a function of time for sample temporal scales: $s=10$ min (

**top**), $s=60$ min (

**middle**), and $s=360$ min (

**bottom**). Each point on the horizontal axis represents a non-overlapping seven-day-long moving window. Asset prices have been expressed in BTC, therefore any BTC-related contribution has been filtered out.

**Figure 16.**Mean lagged q-dependent detrended cross-correlation coefficient ${\rho}_{q}(s,\tau )$ as a function of time after averaging over all the considered cryptocurrencies other than BTC and ETH. Time series representing BTC and ETH returns have been advanced (green) or delayed (red) by $\tau =1$ min and compared with the original non-shifted time series (orange). Two values of the filtering parameter q are shown: $q=1$ (all fluctuations enter with the same weight, the first and third panels) and $q=4$ (large fluctuations are amplified, the second and fourth panels).

**Figure 17.**Temporal co-evolution of BTC price in USD (maroon) and the S&P500 index (blue) over the years 2020–2021. Periods, in which ${\rho}_{q}\left(s\right)$ calculated for these two assets exceed a threshold of 0.25 for $s=360$ min and $q=1$ (see Figure 18), are denoted by grey vertical strips. Specific market events are indicated by Roman numerals: I—the all-market surge at the COVID-19 pandemic onset in March–April 2020, II—the second pandemic wave in June–July 2020, III—a market rally and the following drawdowns in September–October 2020, IV—the cryptocurrency market rally in March–April 2021, and V—a surge and a subsequent rally in September–October 2021.

**Figure 18.**The q-dependent detrended cross-correlation coefficient ${\rho}_{q}\left(s\right)$ calculated in 10-day-long moving windows with a 1-day step for BTC and the traditional market assets: the S&P500 index (blue), crude oil price (CL, black), copper price (HG, brown), gold price (XAU, yellow), and a few regular currencies expressed in the US dollars: euro (EUR, cyan), Swiss franc (CHF, orange), Canadian dollar (CAD, light green), Japanese yen (JPY, magenta), and Norwegian krone (NOK, red). Two temporal scales s ($s=10$ min in the first and third panels, and $s=360$ min in the second and fourth panels) and two filtering parameter q values ($q=1$ in the first and second panels, and $q=4$ in the third and fourth panels) are shown. The horizontal dashed line at ${\rho}_{q}\left(s\right)=0.25$ in the second panel denotes a discrimination threshold applied to determine the shaded regions in Figure 17.

**Figure 19.**Minimal spanning trees calculated from a distance matrix ${\mathbf{D}}_{q}\left(s\right)$ based on ${\rho}_{q}\left(s\right)$ for $q=1$ and $s=10$ min. The data used to create MSTs consists of cryptocurrencies (BTC, ETH, DASH, EOS, and XMR), regular currencies (AUD, GBP, NZD, MXN, ZAR, CNH, EUR, CHF, JPY, CZK, NOK, CAD, and PLN), commodities (gold-XAU, silver-XAG, copper-HG, and crude oil-CL), as well as stock market indices (S&P500-SP, NASDAQ100-NQ, Russel 2000, FTSE, DAX, NIKKEI, and DJIA) in 10-day-long moving windows ended at specific dates: (

**a**) 31 March 2020 (highly correlated markets during the pandemic onset in the United States), (

**b**) 19 May 2020 (maximum cross-market correlations), (

**c**) 28 January 2021 (the GameStop short squeeze related market turbulence accompanied by the cryptocurrency market decoupling), (

**d**) 9 March 2021 (the elevated market cross-correlations), (

**e**) 30 July 2021 (the cryptocurrencies starting a rally phase with minimum cross-market correlations), and (

**f**) 4 October 2021 (the latest phase of the cross-market correlations).

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**MDPI and ACS Style**

Kwapień, J.; Wątorek, M.; Drożdż, S. Cryptocurrency Market Consolidation in 2020–2021. *Entropy* **2021**, *23*, 1674.
https://doi.org/10.3390/e23121674

**AMA Style**

Kwapień J, Wątorek M, Drożdż S. Cryptocurrency Market Consolidation in 2020–2021. *Entropy*. 2021; 23(12):1674.
https://doi.org/10.3390/e23121674

**Chicago/Turabian Style**

Kwapień, Jarosław, Marcin Wątorek, and Stanisław Drożdż. 2021. "Cryptocurrency Market Consolidation in 2020–2021" *Entropy* 23, no. 12: 1674.
https://doi.org/10.3390/e23121674