# The Structural Role of Smart Contracts and Exchanges in the Centralisation of Ethereum-Based Cryptoassets

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Four Tokens Used as DeFi Collateral

**Ampleforth (AMP)**: An algorithmic stablecoin pegged to the US Dollar (USD). It achieves its stability by adapting its supply to price changes without a centralised collateral. The protocol receives exchange rate information from trusted oracles on USD prices and changes the number of tokens that each user holds automatically [16]. AMP was launched in June 2019 and had a market capitalisation close to USD 90M in May 2022 [17].

**Basic Attention Token (BAT)**: A utility token designed to improve efficiency in digital advertising via its integration with the Brave web browser. Users are awarded BAT tokens for paying attention to online advertisements. BAT’s value proposition allows users to maintain control over quantity and type of the advertisements they consume, while advertisers benefit from better user targeting and reduced fraud rates [18]. BAT had an initial coin offering (ICO) in May 2017, and as of May 2022 it had a market capitalisation close to USD 600M which placed it among the top 100 cryptocurrencies [17].

**Dai (DAI)**: A multi-currency pegged algorithmic stablecoin token [19] launched in 2017 which uses, as AMP, smart contracts on the Ethereum network to keep its value as close as possible to the US dollar. Users can deposit ETH as a collateral and obtain a loan in DAI. The stability of DAI is achieved by controlling the type of accepted collateral, the collaterisation ratio and interest rates. In November 2019, DAI transitioned from a single-collateral model (ETH) to a multi-collateral model with many more tokens and stablecoin, some of them, such as BAT and UNI, are analysed in this paper. As of May 2022 DAI had a market capitalisation close to USD 6B, which placed it within the top 20 cryptocurrencies [17].

**Uniswap (UNI)**: A decentralised finance protocol [20] to exchange ERC-20 tokens on the Ethereum network. Unlike traditional exchanges, it does not have a central, limited order book but rather a liquidity pool: pairs of tokens provided by users (liquidity providers) which other users can then buy and sell. This UNI governance token was launched on September 2020 [20]. This token allows its holders to take part in important decisions regarding Uniswap, and to own a share of the common UNI treasury. It is currently ranked among the top 30 cryptocurrencies with a market capitalisation close to USD 4B in May 2022) [17].

#### 2.2. Transaction Networks in Blockchain

#### 2.3. Deep Dive: Network Construction

#### 2.4. Preferential Attachment

#### 2.5. Deep Dive Methodology

- We extract from a fully synchronised archive Ethereum node all transactions from the Ethereum blockchain involving transfers of tokens.
- We build the corresponding directed transaction networks for four DeFi-relevant tokens: Ampleforth (AMP), Basic Attention Token (BAT), DAI and Uniswap.
- We calculate the correlation between in- and out-degree distributions both for all nodes in the network and for high-degree nodes to see whether high-degree nodes are more correlated.
- We compare in- and out-degree distributions with potential best fit functions for the degree distributions.
- We study the centralisation of the network, analysing the preferential attachment to identify the role of hubs. We use the K–S distance between the empirical degree distributions and a power law degree distribution in the range [0, 2.5] for all tokens using the rank function to identify the K–S distance between the empirical cumulative distribution function (ECDF) and the theoretical CDF function.
- We explore the evolution throughout time of the of the value of $\alpha $ in the rank function to confirm the super-linear attachment in the transaction networks.
- We calculate how the density, i.e., the number of edges, grows with the growth in size of the network to confirm our preferential attachment study.
- We study network dismantling by removing up to 200 addresses (represented as nodes in the network) with the highest degree, and we observe how the network is impacted via the Largest Strongly Connected Component (LSCC) over network size ratio. For this, we use three strategies based on the type of node to remove.
- We study the evolution of the scalar assortativity of the transaction networks during dismantling.

#### 2.6. Multilayer Network-Based Methodology

- We measure the initial size of the resulting networks in terms of number of nodes and plot the histograms of its distribution.
- We calculate the distribution of the initial LCC over network size ratio for ${T}^{\prime}$ and ${E}^{\prime}$ to characterize the different networks.
- We perform a similar exercise in each layer after 100 highest degree iterative node removals in the other layer to observe how dismantling takes place in each network.
- We explore the relation between the LCC over network size ratio reached after dismantling in the Ether and the token network.
- We study the relation between the degrees of a node in different layers.

#### 2.7. Bird’s Eye Methodology

- We plot the Jaccard Index between every token network T and the one of Ether E. We do this pairwise for every one of our tokens.
- We analyse the in-degrees of the 2432 token networks using the model selection for power law fits proposed by Alstott et al. [35]) in 2014.
- We propose a novel similarity measure that is order-sensitive and potentially useful for our case of networks with very different sizes, and we test its meaningfulness using a set of randomized null models.
- We draw a heat map with this new similarity measure between all analysed tokens.
- We plot the histograms of the distributions of both the Jaccard Index and our new similarity metric, called Ordered Jaccard, measured between every individual token and Ether, and we calculate their correlation.
- We research potential similarity drivers: network size and market capitalisation. We calculate their correlation.
- We plot network size and the Jaccard and Ordered Jaccard Indexes between the Ether and token networks to identify any potential correlation. Here we start to detect a pattern.
- We perform a similar exercise with the maximum market capitalisation reached by every token network.
- We study the relation between Ether and a specific token and that token with all other Ethereum-based tokens via the Ordered Jaccard Index.
- We explain the methods that we follow to identify addresses belonging to exchanges and smart contracts.
- We plot the percentage of exchanges and smart contracts in the top 100 high-degree nodes.
- Finally, we plot a histogram with the reappearance frequency of dismantled nodes across networks.

## 3. Results

#### 3.1. In- and Out-Degree Correlation

#### 3.2. Power Law Fit

#### 3.3. Preferential Attachment

#### 3.4. Network Dismantling

#### 3.5. Assortativity

#### 3.6. Multilayer Network Dismantling

#### 3.7. Bird’s Eye View of Ethereum-Based Tokens

`t0x8d12a197cb00d4747a1fe03395095ce2a5cc681`) which occurs in more than 1000 networks, or IDEX 1 Exchange (address:

`0x2a0c0dbecc7e4d658f48e01e3fa353f44050c208`), a very popular decentralised exchange, or an exchange Hotbit (address:

`0x274f3c32c90517975e29dfc209a23f315c1e5fc7`) with 402 presences across different tokens and addresses. On the other hand, some of the most active addresses are hard to identify, with no official flags and labels. For example, we find a smart contract (address:

`0x74de5d4fcbf63e00296fd95d33236b9794016631`) with just 19 transactions in Ether but with more than 11M ERC-20 transactions at the time of writing. The very fact that such an important address could leave no recognizable trace of its identity, purpose or origin is a good testimony of the current challenges to the scientific and forensic analysis of public blockchains.

## 4. Discussion

- First, in our deep dive, we observed a slightly super-linear preferential attachment coefficient (${\alpha}^{in}>1.0$), that is persistent throughout time. This implies that few nodes attract a majority of connections from new nodes. This resembles a form of “winner takes all” effect, commonly observed in social systems as well [48]. We identified the relevance of smart contracts and exchanges when we dismantled the resulting transaction networks following selective strategies with a special focus on SC and exchanges.
- Second, we studied a larger set of tokens and focused only on non-zero Ether and token transactions in networks that share at least 10k addresses with the Ether network. We used a multilayer network approach and tried to dismantle a specific layer (aspect) based on selective node-related information coming from a different layer (aspect). Although we confirmed again the relevance hubs when dismantling the layers, we abandoned this research path due to the big size difference between token networks and the Ether transaction network.
- Third, we broadened our lens and study similarities in all transaction networks with at least 10k addresses. For this, we came up with a new index, the Ordered Jaccard Index, that facilitated and confirmed our findings regarding the structural role of SC and exchanges in these networks. We completed our analysis by identifying a degree of correlation between this new index and network size and even market capitalisation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SC | smart contracts |

EOA | Externally Owned Accounts |

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**Figure 1.**Empirical node in-degree and out-degree PDF (Probability Density Function) and CCDF (Complementary Cumulative Distribution Function) for each token plotted, together with the fitted values. To provide a better comparison, we always use fitted power laws as reference, even when they are not the best model as in Table 3. We notice the outliers in DAI out-degree distribution that make the best fit deviate from the power law and the distance between fitted CCDF and empirical CCDF for in-degrees of AMP, which might be caused by the smaller size of this network compared to the others. These are the cases where we encounter the smallest ${x}_{min}$ for our fits as well.

**Figure 2.**K-S distance between the empirical degree distribution and a power law degree distribution for the preferential attachment coefficients ${\alpha}^{in}$ and ${\alpha}^{out}$ in the range $[0,2.5]$ for all four tokens. Minimum values for all four tokens are achieved around $1.0$ for the out-degree and around $1.1$ for the in-degree which indicates super-linear preferential attachment.

**Figure 3.**Evolution of the best fit for the in-degree ${\alpha}^{in}$ (

**top**panel) and out-degree ${\alpha}^{out}$ (

**bottom**panel) preferential attachment coefficients for all four tokens. We used disjoint and non-cumulative time windows to define sub-networks on which we calculate the preferential attachment. Both ${\alpha}^{in}$ and ${\alpha}^{out}$ are almost always above $1.0$ throughout the time period studied, which indicates the persistence of the super-linear preferential attachment.

**Figure 4.**Network density as a function of network size N. The addition of new nodes to the network does not densify the network. The number of edges scales as $d\propto {N}^{-1}$. Each new node adds only a limited number of new edges. This is in line with the observed preferential attachment.

**Figure 5.**Dismantling of the Largest Strongly Connected Component (LSCC) in the transaction networks of the four tokens based on removing the nodes with the highest in-degree. We follow three strategies: first, we only remove nodes that correspond to smart contracts and known exchanges addresses; second, we remove nodes corresponding to EOA addresses; and third, we iteratively remove the highest degree nodes regardless of their address type (a “greedy” strategy, included here as benchmark). The removal of the nodes corresponding to the smart contract and known exchange addresses causes the fastest dismantling compared to EOA. This highlights the important structural role played by these addresses in the network.

**Figure 6.**Evolution of the assortativity for in-degree of the transaction networks during dismantling. We follow the three strategies described in Figure 5. Initial assortativity in the four tokens is slightly negative, probably because most of the low in-degree nodes connect to large hubs and have few connections between themselves. This is why removing EOA nodes during the dismantling, which tend to have lower degree than smart contracts and exchanges, does not affect assortativity at all. However, the removal of smart contracts and known exchange nodes increases assortativity. It makes the network almost non-assortative, as many connections to these high-degree central nodes are removed.

**Figure 7.**Size of the network layers ${E}^{\prime}$ and ${T}^{\prime}$ participating in the multilayer networks in terms of number of nodes (addresses) and their number of occurrences for each of the tokens considered.

**Figure 8.**Histograms of the initial LCC over network size ratio for ${T}^{\prime}$ and ${E}^{\prime}$. In the panels below, we analyse the difference $\Delta $, $LC{C}_{0}/N$ − $LC{C}_{100}/N$ to identify how much this ratio changes after dismantling one hundred nodes (of ${T}^{\prime}$ and ${E}^{\prime}$) with Ether-first (

**bottom left**) and token-first (

**bottom right**) strategies, respectively.

**Figure 9.**

**Left**: LCC over initial network size ratio plotted for ${E}^{\prime}$ and ${T}^{\prime}$ computed for multilayer networks built with shared addresses between ${E}^{\prime}$ and ${T}^{\prime}$. We calculate a Pearson correlation of −0.17.

**Right**: Plot of the $\Delta $s of LCC over network size for token and Ether networks reached after using the Ether-first and token-first dismantling. We obtain a correlation of 0.32.

**Figure 10.**The degree correlation between the two multilayer networks ${E}^{\prime}$ for Ether and ${T}^{\prime}$ for token consisting only of addresses $a\in E\cap T$.

**Figure 11.**Degree correlation $\rho $ between the two multilayer networks ${E}^{\prime}$ and ${T}^{\prime}$ plotted against the $\Delta $ of the LCC over network size ratio. This $\Delta $ refers to the portion of the LCC over network size ratio dismantled in ${E}^{\prime}$ and ${T}^{\prime}$. The Pearson correlation between $\rho ({E}^{\prime},{T}^{\prime})$ is, respectively, 0.532750 and 0.505823.

**Figure 12.**Histograms of the distribution of Jaccard Index J between the top 100 high-degree nodes (“greedy” dismantling order) for Ether and analysed tokens (

**top**plot); plot of the Ordered Jaccard Index ${O}_{j}$ (

**mid**plot); plot of ${O}_{j}$ and J (

**bottom**plot); the correlation between ${O}_{j}$ and J is, as expected, high, 0.912, but not fully coinciding. This seems to justify the new measure.

**Figure 13.**To verify the validity of our proposed similarity metric, we test it against a null model where addresses are randomly drawn with the same frequency that we observe in the real data of 161,000 addresses. We then take every time 2432 buckets of addresses for the tokens plus one additional for the native cryptocurrency Ether. We repeat this random draw 10 times and then compare the resulting null model with the real one in a Cumulative Distribution Function (CDF) plot. We do this for the normal Jaccard Index J, and for the Ordered Jaccard Index ${O}_{j}$. The real data we have are well discernible from purely random curves for both metrics: random data is much more concentrated, while real data follows a much softer slope, with values arriving up to 0.08 for the Jaccard Index J and 0.25 for the Ordered Jaccard ${O}_{j}$, while all simulated attempts displayed are much more skewed towards 0 and stop earlier in the metric. The difference, not present in other tested metrics, strongly suggests that we are measuring with both the Jaccard and the Ordered Jaccard Indexes a fundamental property of our data set and not just a random number. Additionally, the Ordered Jaccard Index seems to distinguish clearer between real data and null models.

**Figure 14.**Heat map with the Ordered Jaccard Index ${O}_{j}$ between all 2432 tokens. Tokens have been ordered according to their average $\langle {O}_{j}\rangle $ with all the other tokens.

**Figure 15.**Network size as number of addresses N and maximum market capitalisation reached in USD. Since we are dealing with cumulative networks, the maximum market capitalisation ever reached compounds for all the previous network growth. We obtain a Pearson correlation $\rho $ of 0.3318.

**Figure 16.**We plot the Jaccard Index J and the Ordered Jaccard Index ${O}_{j}$ between the 100 highest-degree nodes in “greedy” dismantling order between the individual token and Ether against the network size N (

**top**plots) and the maximum market capitalisation ever recorded in the token history (

**bottom**plots).

**Figure 17.**We plot the Ordered Jaccard Index ${O}_{j}$ between Ether and a specific token with the average $\langle {O}_{j}\rangle $ for that token with all other Ethereum-based tokens. The measured correlation Pearson correlation $\rho $ reaches 0.674613. It confirms the relevance of this metric as a general measure of similarity between tokens.

**Figure 18.**Number of first 100 higher degree nodes in greedy dismantling order that can be labelled as exchange according to information from

`etherscan.io`.

**Figure 20.**Reappearance frequency of dismantled nodes between different token networks (plus Ether), i.e., in how many different networks the individual addresses are appearing.

**Table 1.**Summary of the data sets used in this analysis, including block range and time span for each token. These cover the time span since the creation of each token, with the exception of DAI. The launch of DAI took place in 2017, but we only use transactions since its transition to a multi-collateral model in 2019.

Token | Tx | Nodes | Edges | Blocks | Time Span |
---|---|---|---|---|---|

AMP | 755,827 | 83,050 | 201,456 | 7,953,823–12,500,000 | 14 June 2019–25 May 2021 |

BAT | 3,046,615 | 1,105,958 | 1,702,429 | 3,788,601–12,500,000 | 29 May 2017–25 May 2021 |

DAI | 8,422,158 | 1,042,638 | 2,523,076 | 8,928,674–12,500,000 | 13 November 2019–25 May 2021 |

UNI | 2,079,132 | 701,054 | 1,271,933 | 10,861,674–12,500,000 | 14 September 2020–25 May 2021 |

**Table 2.**Spearman correlation ${\rho}_{s}$ between in-degree ${k}_{in}$ and out-degree ${k}_{out}$ for the four tokens. The relation is stronger for AMP and DAI than for BAT and UNI. However, we observe an irregular pattern for all nodes. We suspected that the correlation for nodes with degrees over 100 could even be stronger. Computing the Spearman correlation for ${k}_{in}>100$ confirmed this point.

Token | ${\mathit{\rho}}_{\mathit{s}}({\mathit{k}}_{\mathit{in}},{\mathit{k}}_{\mathit{out}})$ | p-Value | ${\mathit{\rho}}_{\mathit{s}}({\mathit{k}}_{\mathit{in}},{\mathit{k}}_{\mathit{out}})$ Where ${\mathit{k}}_{\mathit{in}}>100$ | p-Value |
---|---|---|---|---|

AMP | 0.5201 | 0 | 0.6772 | 1.2470 $\times {10}^{-7}$ |

BAT | 0.1523 | 0 | 0.4119 | 2.6450 $\times {10}^{-13}$ |

DAI | 0.4842 | 0 | 0.4874 | 5.112 $\times {10}^{-48}$ |

UNI | 0.2710 | 0 | 0.5094 | 1.3512 $\times {10}^{-15}$ |

**Table 3.**Power law fit for the in- and out-degree distributions of the four tokens. The exponent $\gamma $ of the power law degree distribution ${p}_{k}\sim {k}^{-\gamma}$ typically fulfils $2\le \gamma \le 3$ for the network to be characterized as scale-free [35,37]. This condition occurs only for the in-degree ${k}_{in}$ of AMP and out-degree ${k}_{out}$ of DAI, which suggests that for most of our cases the conditions for a scale-free network are weak [38]; ${x}_{min}$ is the minimum x value where the fit starts. The table also includes the standard error $\sigma $ for all coefficients to facilitate the assessment of the fit.

Token | k | ${\mathit{x}}_{\mathit{min}}$ | $\mathit{\gamma}$ | $\mathit{\sigma}$ | d | Best Fit |
---|---|---|---|---|---|---|

AMP | ${k}_{in}$ | 3.0 | 2.9254 | 0.0169 | 0.0362 | Power Law |

AMP | ${k}_{out}$ | 13.0 | 1.6150 | 0.0409 | 0.0395 | Power Law |

BAT | ${k}_{in}$ | 44.0 | 1.7677 | 0.0330 | 0.0292 | Power Law |

BAT | ${k}_{out}$ | 58.0 | 1.6580 | 0.0326 | 0.0304 | Truncated Power Law |

DAI | ${k}_{in}$ | 57.0 | 1.8552 | 0.0240 | 0.0115 | Power Law |

DAI | ${k}_{out}$ | 4.0 | 2.5021 | 0.0055 | 0.0121 | Lognormal |

UNI | ${k}_{in}$ | 51.0 | 1.7812 | 0.0409 | 0.0271 | Power Law |

UNI | ${k}_{out}$ | 29.0 | 1.6591 | 0.0299 | 0.0300 | Power Law |

**Table 4.**The ${\alpha}^{in}$ and ${\alpha}^{out}$ for each of the four analysed tokens and their errors. All values of $\alpha $ are higher than 1, indicating a super-linear preferential attachment.

Token | ${\mathit{\alpha}}^{\mathit{in}}$ | Error | ${\mathit{\alpha}}^{\mathit{out}}$ | Error |
---|---|---|---|---|

AMP | 1.05 | 0.143 | 1.02 | 0.174 |

BAT | 1.15 | 0.198 | 1.1 | 0.226 |

DAI | 1.1 | 0.099 | 1.05 | 0.126 |

UNI | 1.05 | 0.227 | 1.02 | 0.257 |

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**MDPI and ACS Style**

De Collibus, F.M.; Piškorec, M.; Partida, A.; Tessone, C.J.
The Structural Role of Smart Contracts and Exchanges in the Centralisation of Ethereum-Based Cryptoassets. *Entropy* **2022**, *24*, 1048.
https://doi.org/10.3390/e24081048

**AMA Style**

De Collibus FM, Piškorec M, Partida A, Tessone CJ.
The Structural Role of Smart Contracts and Exchanges in the Centralisation of Ethereum-Based Cryptoassets. *Entropy*. 2022; 24(8):1048.
https://doi.org/10.3390/e24081048

**Chicago/Turabian Style**

De Collibus, Francesco Maria, Matija Piškorec, Alberto Partida, and Claudio J. Tessone.
2022. "The Structural Role of Smart Contracts and Exchanges in the Centralisation of Ethereum-Based Cryptoassets" *Entropy* 24, no. 8: 1048.
https://doi.org/10.3390/e24081048