3.1 Data

The cryptocurrency data are obtained from the website www.coinmarketcap.com. We take into account daily prices and volumes. We initially considered all available coins listed within the sample period from January 1, 2015, till December 31, 2022 (2922 days). Several filters are applied to consider a given cryptocurrency in the final dataset: (1) each crypto included in the dataset was among 100 cryptocurrencies with the highest capitalization on any day during the sample period. Such a filter allowed us to omit small—in terms of market capitalization—assets; (2) we introduced the condition related to the number of days a crypto is required to be listed. It differentiates between the three approaches. In the case of one network built over the whole period, the minimum was 2338 days, which accounts for 80% of the full sample period. In the case of two-year periods, we required the data for the whole period, while for the networks based on daily snapshots 180 days of returns were taken into account; (3) price data are available with no more than 30 missing observations. These steps allowed us to include both active and inactive coins, thus avoiding the survivorship bias. Such an approach allows us to include those cryptos that were most active in trading, even if this activity was only temporary and later they were no longer available on the market.

The coin selection procedure enables us to focus on the main players in the market without narrowing the circle of currencies to the most well known among them. We take into account all cryptocurrencies, among them those which are performing different roles as payment cryptocurrencies (coins), utility tokens, decentralized finance and stablecoins (we follow here the division of crypto assets provided by the Corporate Finance InsituteFootnote ²). Stablecoins are often removed from academic studies because of their special features—they are pegged to a stable asset such as traditional currencies, commodities (e.g. gold) or financial algorithms. Due to that fact, their volatility is much smaller than the remaining crypto assets. Taking stablecoins into account allows us to improve the interpretation of the network structure (Ling et al., Reference Li, Li, Long and Wang2022).

The full list of cryptocurrencies is available upon request. The list of digital currencies which appear on the graphs in the paper is in Table 2 in the Appendix. Each network consists of nodes, which are individual cryptocurrencies, and the edges are calculated as distances based on returns’ correlations. We have 755 different crypto assets in the database, which follow the mentioned criteria. For all cryptocurrencies in the dataset, we calculate returns and the Kendall $\tau$ correlations between returns of each pair of crypto assets. Based on these, we calculate the Euclidean distances. In each of the approaches, the whole period, two-year periods or each day networks, the number of cryptocurrencies in networks differs.

3.2 Methods

We construct weighted undirected networks within three approaches: first, a one-time approach where one network for the entire sample period is constructed. Second, we obtain four networks, each based on two years of data. Third, we apply a day-by-day approach in which each network is created every day in the sample.

While various econometric tools exist for analyzing financial time series dependencies, network analysis offers a uniquely comprehensive perspective. Though traditionally more prevalent in other disciplines, this approach provides deep insights into complex systems with multiple interconnected elements in finance. When constructing a network, we rely on the correlation matrices and distances for crypto returns as this is a standard solution for networks in the financial series (Boginski et al., Reference Boginski, Butenko and Pardalos2005; Wu et al., Reference Wu, Zhao and Zheng2021). We assume that for a currency to be considered as the central one, it must be highly connected to other crypto assets. The stronger the relationships with other cryptos, measured by correlations, the more important (and more central) a given cryptocurrency is in the network. We consider a weighted network using an undirected graph $G=(V, E, d)$ , where $V$ is the set of $N$ nodes, $E$ the set of $N \times N$ edges, and $d$ is the weight function assigned to the edges. Here, the nodes correspond to different cryptocurrencies, and the edges between them carry weights indicative of the strength of connections between these cryptocurrencies.

The procedure of constructing a network consists of several steps. First, we obtain Kendall’s correlations $\tau _{ij}$ between two series of returns of cryptocurrencies, $i$ and $j$ . The returns are calculated as $r_i=\ln (P_t/P_{t-1})$ , where $r_i$ stands for the daily return of asset $i$ , while $P_t$ and $P_{t-1}$ are the coin’s prices on day $t$ and $t-1$ , respectively. Then we filter significant correlations, thus leaving only those that are nonzeros from the statistical point of view.

Additionally, following Plerou et al. (Reference Plerou, Gopikrishnan, Rosenow, Amaral, Guhr and Stanley2002) and Giudici and Polinesi (Reference Giudici and Polinesi2021), we apply the RMT approach, which allows us to remove noise from the correlation matrix. There is a general agreement that the correlation matrix might contain not only information but also noise (Onnela, Kaski and Kertész, Reference Onnela, Kaski and Kertész2004) and that RMT is a well-performing tool to handle the complexity of high-dimensional data as it analyses the distribution of eigenvalues. Specifically, the presence of large eigenvalues indicates dominant patterns, that is, the “market” component (Laloux et al., Reference Laloux, Cizeau, Potters and Bouchaud2000; M. Potters, Reference Potters, Laloux and Bouchaud2005).

We test the null hypothesis that the eigenvalues of the correlation matrix match those of a symmetric random Wishart matrix of equal size (Miceli and Susinno, Reference Miccli and Susinno2004), against the alternative hypothesis that the eigenvalues differ. For $N,T \rightarrow \infty$ , where $N$ is a number of variables (cryptocurrencies) and $T$ is a length of the time series, with $ Q=T/N \geq 1$ , the spectral density $P_{rm}$ of eigenvalues $\lambda$ is given by:

\begin{equation*} P_{rm}=T/2\pi \frac {\sqrt {(\lambda _{+}-\lambda )(\lambda -\lambda _{-})}} {\lambda } \end{equation*}

where

\begin{equation*} \lambda ^+_- = 1+1/Q \pm 2*\sqrt {1/Q}.\end{equation*}

From the $P_{rm}$ , it follows that if $\lambda _k \ge \lambda _{+}$ , then the $k$ -th empirical eigenvalue cannot be an eigenvalue from a random Wishart matrix, and the null hypothesis is rejected. For every correlation matrix of crypto returns, we obtain $\lambda _{+}$ and verify if the highest eigenvalues exceed this value.

We then retain only those eigenvalues that are equal or exceed $\lambda _{+}$ and reconstruct the correlation matrix through singular value decomposition (Plerou et al., Reference Plerou, Gopikrishnan, Rosenow, Amaral, Guhr and Stanley2002). To preserve the sum of all the eigenvalues, we replace all the eigenvalues lower than $\lambda _{+}$ with their average. This allows us to “clean” the correlation matrix of noise while maintaining the same trace of the matrix (Plerou et al., Reference Plerou, Gopikrishnan, Rosenow, Amaral, Guhr and Stanley2002; Miceli and Susinno, Reference Miccli and Susinno2004). The matrices, “filtered” in this way, are used in the next steps.

Since the correlation coefficient of a pair of crypto returns itself is not a proper measure of the distance between the two series,Footnote ³ we calculate distances based on the “filtered” matrices for all pairs of cryptocurrencies. For this transformation, we calculate Euclidean distances based on the following formula: $d_{ij} = \sqrt{2*(1-\tau _{ij})}$ (Onnela, Kaski and Kertész, Reference Onnela, Kaski and Kertész2004; Di Matteo, Pozzi, and Aste, Reference Onnela, Kaski and Kertész2010). In the next step, the matrix of distances $d_{ij}$ is used as the weighted adjacency matrix of the network $G$ .

To obtain a complex system with several centers, we apply the MST approach, proposed in a similar framework by Mantegna (Reference Mantegna1999), which limits the number of connections between the nodes. A spanning tree is a simply connected acyclic graph that connects all $N$ nodes (cryptocurrencies) with $N-1$ edges in such a way that the sum of all edges’ weights, $\sum _{ij}{d_{ij}}$ , is minimized.

MST allows selecting the most relevant connections between the crypto assets in the set (Ho, Chiu, and Li, Reference Onnela, Kaski and Kertész2020 ; Zięba, Kokoszczyński, and Śledziewska, Reference Zięba, Kokoszczyński and Şledziewska2019; Vidal-Tomás, Reference Onnela, Kaski and Kertész2021). Moreover, to obtain a clear structure we set the limit for a correlation, for which the dependence between crypto assets is considered (Karim et al., Reference Karim, Naeem, Hu, Zhang and Taghizadeh-Hesary2022). In the literature, this is known as the WTA approach, which requires establishing a correlation threshold. The WTA method allows us to reduce the number of edges in the network by omitting those of minor importance and focusing on the significant (highly correlated) ones. As explained by Giudici et al. (Reference Giudici, Hadji-Misheva and Spelta2020) the detection of patterns requires such a representation of the network, which replaces complexity with scarcity. It is achieved here by reducing the number of edges and leaving only those of the greatest importance. In our study, following Tse, Liu, and Lau (Reference Tse, Liu and Lau2010) and Heiberger (Reference Heiberger2014), we apply the threshold of $\tau \ge 0.4$ .

For the obtained networks, we calculate standard centrality measures such as degree, betweenness, closeness and eigenvector centrality. It offers us a description in several dimensions: degree indicates highly connected nodes, betweenness highlights nodes that are right in the middle, closeness indicates how quickly information can spread from a node to all others, while eigenvector centrality takes into account the importance of nodes’ neighbors (Oggier and Datta, Reference Oggier and Datta2021). In our framework, those measures combine correlation information into four metrics.

In our weighted network framework, the degree centrality of a node is a crucial attribute. It considers the sum of weights associated with edges incident to a node. It is computed using the formula:

\begin{equation*}D_i = \sum _{j}{d_{ij}}.\end{equation*}

When it comes to betweenness centrality, the concept of shortest paths is necessary. The shortest path between two nodes is the path with the shortest length calculated as the minimum total weight among all possible paths connecting those nodes. Formally, the betweenness centrality $B_i$ of a node $i$ is calculated as the fraction of shortest paths between all pairs of nodes $h$ and $j$ that pass through node $i$ (say $s_{hj}(i)$ ), divided by the total number of shortest paths between $h$ and $j$ (say $s_{hj}$ ):

\begin{equation*}B_i = \sum _{h,j} \frac {s_{hj}(i)}{s_{hj}}.\end{equation*}

This measure considers both the presence and the strength of connections between nodes when evaluating the influence of a node within the network.

Closeness centrality is the inverse of the average shortest length from one node to each other node. Specifically, for node $i$ it is the inverse of the average length of the shortest paths between node $i$ and any other node $j$ :

\begin{equation*}C_i = \frac {N-1}{\sum _{j}{d_{ij}}}.\end{equation*}

The inverse is used so that a higher closeness centrality indicates a more desirable centrality score.

In a weighted network, eigenvector centrality measures the influence of a node based on both the number and the importance of its neighbors. It assigns higher centrality to nodes that are connected to other nodes that themselves have high centrality. Mathematically, eigenvector centrality $ E_i$ for a node $ i$ is calculated using the formula:

\begin{equation*}E_i = \frac {1}{\lambda } \sum _{j} d_{ij} e_j\end{equation*}

where $\lambda$ represents the largest eigenvalue of the distance matrix, $d_{ij}$ represents the weight of the edge between node $i$ and node $j$ , and $e_j$ represents the corresponding eigenvector component associated with node $j$ .

Each of those four measures captures a different feature of centrality. As a result, each measure indicates different nodes as the most central and important ones. Therefore, we applied a procedure which captures information gathered by these measures and allows us to indicate a unified ranking. This ranking is applied to the series of centrality measures obtained for daily networks.

For all cryptocurrencies listed in a given period, we compute four centrality measures based on the distances obtained in the moving window of 180 days. Then we apply the Technique for Order of Preference by Similarity to an Ideal Solution (TOPSIS) with entropy weights for identifying the most influential nodes in a similar vein as described by Dwivedi and Sharma (Reference Dwivedi and Sharma2023) and Alao et al. (Reference Alao, Ayodele, Ogunjuyigbe and Popoola2020), among others. Entropy-weighted TOPSIS method is a multi-criteria decision-making approach that allows us to find the best option from a set of node alternatives (here cryptocurrencies, $i = 1, \dots , N$ ) based on predefined criteria (here the four centrality measures, $j = 1, \dots , 4$ ). This approach helps ensure that the most informative measures contribute more to the decision-making process, leading to more robust rankings. The applied algorithm consists of six steps:

(1) The normalization of the centrality measures in the decision matrix

\begin{equation*} x_{ij}^* = \frac {x_{ij}}{\sqrt {\sum _{i=1}^{N} (x_{ij})^2}} \end{equation*}

where $ x_{ij}$ represents the value of centrality measure $ j$ for node $ i$ and $ N$ is the total number of nodes.

(2) The calculation of weights based on the information entropy for each centrality measure, so that the bigger the value of the entropy weight of the measure, the more useful the information of the measure

\begin{equation*} w_j = \frac {1 - H_j}{\sum _{j=1}^{4} (1 - H_j)} \end{equation*}

where $ H_j = -\frac{1}{\log (N)}\sum _{i=1}^{N} p_{ij} \log (p_{ij})$ is the entropy of centrality measure $ j$ and $ p_{ij} = \frac{x_{ij}^*}{\sum _{i=1}^{N} x_{ij}^*}$ . Note that $\sum _j w_j = 1$ .

(3) The computation of the entries of the weighted normalized decision matrix:

\begin{equation*}v_{ij} = x_{ij}^* \times w_j.\end{equation*}

(4) The determination of the best and the worst solution

\begin{equation*} A^+_{j} = \max _{i} v_{ij}, \quad A^-_{j} = \min _{i} v_{ij} \end{equation*}

(5) The calculation of the distances of each alternative to the ideal (the best) solution and anti-ideal (the worst) one

\begin{equation*} S_i^+ = \sqrt {\sum _{j=1}^{4} (v_{ij} - A_j^+)^2}, \quad S_i^- = \sqrt {\sum _{j=1}^{4} (v_{ij} - A_j^-)^2}. \end{equation*}

(6) The calculation of the relative closeness degree to an ideal solution for every alternative

\begin{equation*} RC_i = \frac {S_i^-}{S_i^- + S_i^+}. \end{equation*}

(7) The determination of the final ranking by sorting the alternatives from the largest $RC_i$ . It reveals the most important nodes in the network, see Opricovic and Tzeng (2004) among others.

In the empirical part, we present rankings in line with each of the four centrality measures separately and the final ranking which combines all the considered measures through the entropy-weighted TOPSIS method.

The graphs were drawn using the igraph R package https://igraph.org/r/html/1.3.4/mst.html.

4.1 Static networks based on the whole sample period

First, we show the static network created for cryptos that were listed within the period 2015–2022 for at least 2338 days (80% of the whole sample). For such crypto assets, we obtained correlations, that were a basis for distances calculations. We present three scenarios: (1) the MST with $N$ nodes and $N-1$ edges; (2) the network constructed with the WTA approach with 0.4 threshold, and (3) the mix of the MST with the WTA approach. The number of nodes changes depending on the scenarios. In the case of the whole sample, the full graph would consist of 755 nodes, which represent all crypto assets included in our database. As the correlation matrix is symmetric, there would be 284635 edges. By application of the filters (MST or WTA) we remove nonrelevant edges, leaving only those that are the most informative (MST) or represent the strongest dependence (WTA). If we were trying to create a graph based on all cryptocurrencies, which were listed for 8 years uninterruptedly, then we would obtain a graph with several nodes only. Thus when building the first four graphs, we consider all cryptocurrencies, that were listed at least for a given period.

Figure 2 presents networks from scenarios (1) and (2). On the left, we show the graphs built with MST, and on the right, we show the WTA approach. Every node on the circle represents one cryptocurrency. The node size represents the degree – the higher the degree, the bigger the node. The width of edges represents correlations of returns between every pair of nodes, the corresponding weight is the distance between the two nodes inversely proportional to the correlation. The more intense the color of an edge, the higher the correlation. The widths of the edges in the graph range from 0.0 to 0.98. A graph built as MST has only one distinctive node, that is Bitcoin, which has the highest degree (a black dot on the right side of a circle). For the WTA approach, a greater diversity of nodes is obtained. There are more prominent nodes in this case. Also, some areas in the circle are empty suggesting a lack of correlations between some nodes.

Figure 2. Networks with either MST filter or the WTA approach.

Note: For a graph on the left we used the MST filter, while that on the right utilizes the WTA approach with the threshold for correlation coefficient equal to 0.4. The size of the node depends on the centrality degree of a particular node. The width of links represents the strength of the dependence between two nodes measured by the correlation coefficients. The higher the correlation is, the darker the color of the edge. A graph on MST has 160 nodes and 159 edges, while the WTA graph has 21 nodes and 49 edges.

Such separate approaches give only a general picture and do not allow one to observe the hierarchical structure. To deepen the analysis, we have combined both approaches (scenario 3). Reducing the multidimensionality of the dataset within the MST approach and the WTA allows us to make visible several communities (hubs) with central nodes. Figure 3 presents a network with combined MST and WTA approaches. The network exhibits a hierarchical structure, with Bitcoin (BTC) occupying the central position as the node with the highest degree and XRP being the connecting (bridge) node with the LTC community. XRP is designed for fast and low-cost international money transfers, while LTC offers faster and cheaper transactions compared to Bitcoin. Other cryptocurrencies, such as ETC and ETH, form distinct communities around themselves, each serving slightly different purposes within the ecosystem. The ETC community emphasizes immutability and supports decentralized applications, while the ETH stands out as a major hub for smart contracts and decentralized applications.

Figure 3. The network based on the combination of MST and WTA built for the data listed for at least 2338 days of the sample.

Note: The size of nodes is proportional to the degree of each coin. The higher the correlation, the darker the color of the edges. Only the first five crypto assets with the highest degree are labeled with a cryptocurrency ticker. The remaining nodes are plotted as black dots.

The above graphs show that over the whole sample period, from 2015 to 2022, Bitcoin is the undisputable center in the network. There are other important crypto assets in the network, which gather around themselves smaller communities distinct from the rest of the structure. We examine the robustness of these results by looking at graphs built for two-year periods.

4.2 Static networks based on two-year periods

In this part, we rely on crypto assets that were listed for the whole two-year period. The analysis of networks built in two-year periods enables us to assess the dependence between cryptocurrencies in several snapshots. Each of them reflects different steps in the evolution of the cryptocurrency market. The number of cryptocurrencies listed on the markets increased steadily. As shown in Figure 1, the correlations also increased (at least when one compares 2015-2016 with later periods).

Figure 4 shows four networks built based on two-year periods of daily observations when both MST and the WTA approach with the threshold of 0.4 are applied. The network obtained for 2015-2016 is the simplest one among these four, with BTC as a hub and five nodes, CRT, PPC, LTC, NMC, and DOGE linked closely. Each of these cryptos serves different purposes. CRT focuses on multi-currency wallet services, PPC is known for its energy-efficient proof-of-stake mechanism, LTC was already mentioned as a tool for fast and cheap transactions, NMC provides decentralized domain name system and identity services, and DOGE, initially a joke coin, has developed a strong community for tipping and donations. Later, at every two-year period, the network is hierarchical with BTC as the central node with different hubs forming their communities. In the second period, the hubs are LTC, ETH, XMR, SC, and LSK. ETH introduces smart contracts and decentralized applications, XMR focuses on privacy and untraceable transactions, SC provides decentralized cloud storage, and LSK enables decentralized application development with a focus on JavaScript. During the third period, the hubs include again BTC, LTC, and ETH, but the new ones are BCPT, which facilitates blockchain-based credit and debt management, QTUM which combines Bitcoin’s security with Ethereum’s smart contracts for business applications, and POWR which promotes energy trading and sustainability solutions via blockchain. In the fourth period, the hubs are again LTC and SC, but among the new ones are: GRS which focuses on privacy, fast transactions, and low fees, BTH that addresses Bitcoin’s scalability with larger block sizes and faster transactions, and JUV which represents a trend toward sports and entertainment tokens, enhancing fan engagement and interactions.

Figure 4. Networks with both MST filter and the WTA approach in two-year periods based on daily data.

Note: We label only the first five cryptocurrencies in the degree ranking. The higher the correlation, the darker the edge. The higher the degree, the larger the size of a node.

As the market develops, the number of nodes and edges increases. The density of the networks is calculated as the number of actual edges to the number of potential ones decreases in the subsequent periods. It signifies the decreasing connectivity of the market. In the first graph 4(a) representing the network for 2015–2016, we have only 5 nodes and 4 edges. The last one shows 411 nodes and 406 edges. The density decreases from 0.4 in the first subperiod to 0.005 in the last one. Two tickers are present on all four graphs, BTC and LTC, another one, ETH appears in the last two, and the remaining cryptocurrencies change over time. BTC is always lying in the center of the graphs as it is featured by the highest degree (see Table 1). The next is LTC (in 2015–2016, 2017–2018, and 2019–2020) and ETH (in 2021–2022).

Table 1. The degree of the major players among cryptocurrencies in two-year periods

Note: This list presents all cryptocurrencies (in alphabetical order) which tickers appeared on the plots, starting from Figure 3 and ending at Figure 6. The letters, D, B, C, and E display if a given crypto was among the first 10 cryptocurrencies in the daily networks’ ranking presented at Figure 5 and Figure 6 based on the degree, betweenness, closeness, and eigenvector, respectively.

In subsequent two-year periods, the networks get more nodes and edges as we observe more connections between nodes. Thus the nature of the organization of cryptocurrencies changes from a very simple five-node network in the first period, to hierarchical networks with several clusters around nodes. In the last network for the period 2021–2022, we find BTC is taking over most of the connections. It means that the correlations with BTC are on average the highest among all nodes. In the arrangement of the MST, a cryptocurrency network moves from a structured snowflake-like graph to a simpler egocentric graph with BTC as the main node.

4.3 Central nodes in day-by-day snapshots

In this section, we analyze all four measures of cryptocurrencies’ network centrality separately and combined. We consider networks obtained in a moving 180-day window under the condition that pairs of crypto assets have been listed together for at least 90 days. For each day and each coin in the sample, we calculate four centrality measures and create the ranking from the highest value of the centrality measures to the lowest. Figures 5(a)-5(d) report the ranking of cryptocurrencies starting from those with the highest value. For the sake of visibility, only the top 10 cryptos are presented. We highlight in color those cryptocurrencies that took the first three places. As we assign an average for tied ranks, we sometimes obtain intermediate values. Thus we show the first place in red, rank 1.5 (joint first place) in blue, the second place in green, rank 2.5 in violet and the third place in orange.

Concerning the degree, Figure 5(a) shows that Bitcoin was the cryptocurrency with the highest value in 2015 and 2016, but then lost its leading position to other currencies such as LTC, ETH, QTUM, and WETH. After mid-2017, shifts in the ranking often occur daily, demonstrating that the market situation changes rapidly and that cryptocurrencies occupying central positions in the network frequently rotate.

Figure 5. The ranking of cryptocurrencies based on a single centrality measure.

Note: The results for 10 cryptocurrencies with the highest centrality measure in the sample are shown. Bars represent positions in the ranking from the first (red) to the fifth (orange).

Figure 5(b) shows that in the case of betweenness, the changes in the ranking are much less frequent. Crypto that reaches the highest measure of betweenness keeps it for a longer period of time. The characteristic feature, already observed for the previous centrality measure, is that Bitcoin was dominant in 2015 and 2016, but beginning in 2017, it started to lose its position. There was no single dominant player in terms of betweenness centrality measure in the cryptocurrency market during the crisis time in 2018. The second half of 2019 belonged to a stablecoin, USDT (Tether). At the beginning of the COVID-19 pandemic, BTC became again the most central in terms of betweenness, and at the end of the sample, DAI took the first position.

Figure 5(c) makes evidence of the ranking of cryptocurrency concerning the closeness measure. At the outset, BTC appears to have the highest closeness, but it loses position in the ranking around 2016. Later on, changes in the ranking are rapid. The second major cryptocurrency, ETH, was in the first position around 2020. Some patterns are visible—the stablecoins such as XAUT, PAXG, USDC, and USDT are together ranked in third (2021) or second (2022) place.

Figure 5(d) illustrates the ranking of cryptocurrencies for the eigenvector centrality measure over the sample period. For this measure of prestige, changes in ranking occur most frequently. Leaving aside the initial period and prevalence of Bitcoin in 2015, followed by LTC and the return of BTC in the second half of 2016, it is apparent that no single cryptocurrency has maintained a central position for longer than a few weeks. Each cryptocurrency experiences brief periods of prominence, but these are typically short-lived.

The above-discussed centrality measures show slightly different results. In the early days of 2015 and the first half of 2016, Bitcoin seemed to be the undisputed major player. Its relevance disappeared early in 2016, depending on which measure of centrality we use. Several cryptos seem to be dominant in an era of accelerated growth in the cryptocurrency market after the 2018 crisis. In the COVID-19 pandemic, several cryptos appeared to be central in the network, such as Ethereum (degree, eigenvector) or Geminidollar (betweenness).

To indicate a major cryptocurrency, we applied the ranks based on the entropy-weighted TOPSIS method described in Section 3.2. Figure 6 shows the first 10 cryptocurrencies, which are the most often ranked as the first five players. We find that Bitcoin is the most central cryptocurrency in 2015 and 2016. It also appears from time to time among the first five winners in subsequent periods. The next three positions on the list are taken by Tether, USD Coin, and Binance USD (all three are stablecoins). They are leading in the centrality measures’ ranking from mid-2020 until the beginning of 2022. The other two commodity-backed stablecoins, PAX Gold and Tether Gold take over the lead in 2022. Both traditional cryptocurrencies like Ethereum and Lithium are occasionally leaders in the ranking over the whole period.

Figure 6. Entropy-weighted TOPSIS ranking of cryptocurrencies.

Note: The ranking is obtained by the entropy-weighted TOPSIS method considering the four centrality measures: degree, betweenness, closeness, and eigenvector centrality as decision criteria. The results for 10 cryptocurrencies with the highest ranking in the sample are shown. Bars represent positions in the ranking from the first (red color) to the fifth (orange).