On the Ethereum Blockchain Structure: a Complex Networks Theory Perspective

1. Introduction

• Ethereum accounts include smart contracts and externally owned accounts, and their transactions support applications ranging from cryptocurrency exchange to identity management and voting.Ether is used to pay for requested operations executed by the platform's machines.Source: §1 · p. 1
• The authors represent Ethereum accounts as nodes and each recorded transaction as a new link in a complex network.Transactions may transfer cryptocurrency, create a smart contract, or invoke a contract.Source: §1 · p. 1
• Changing the number of blocks used to extract transactions produces networks of different sizes and complexities, influencing their structure.The analysis also uses blockchain history to examine changes in network structure over time.Source: §1 · pp. 1–2
• Most nodes have low degree, but several hubs have higher degrees and may be easier to identify when they are externally owned accounts.The paper frames hubs as important contributors to blockchain evolution and notes their lower level of anonymity [26].Source: §1 · p. 2

2.1. What is a Blockchain

• A blockchain is a distributed ledger of transactions in blocks linked to the preceding block, forming a chronological chain, [11].Transactions within a block are assumed to have occurred at the same time.Source: §2.1 · p. 2
• Cryptographic hashes link subsequent blocks, so changing transaction data alters later block hashes and creates detectable inconsistencies across replicated copies.The paper attributes public, traceable, and tamper-resistant confirmed transactions to the combination of P2P systems, cryptography, consensus, and pseudonymity.Source: §2.1 · p. 2
• Addresses provide pseudonymity: activity under an address is traceable, but linking it to a specific entity or individual is computationally expensive, though not impossible.Source: §2.1 · p. 2

2.2. Ethereum

• Ethereum is a blockchain-based software platform for building and running smart contracts and decentralized applications.It provides a Turing-complete programming language for creating programs that run on the blockchain.Source: §2.2 · p. 2
• Ethereum has externally owned accounts controlled by people and contract accounts controlled by code, with account balances changing through state transitions.Contract code can be triggered by transactions and can generate further transactions; the state is encoded in a Merkle Patricia tree.Source: §2.2 · p. 2
• Ether is the cryptocurrency used to pay other accounts or machines executing requested operations, supporting DApps, smart contracts, tokens, and peer-to-peer payments.The paper also calls Ethereum “programmable money.”Source: §2.2 · p. 2

2.3. Complex Networks Analysis

• Complex network analysis represents entities as nodes and their interactions as links, which may be directed or undirected depending on whether interactions are asymmetric or symmetric.The paper uses this framework to study Ethereum with a set of standard network metrics.Source: §2.3 · p. 2

2.3.1. Number of nodes.

• The number of nodes counts distinct Ethereum accounts involved in transactions in the considered snapshot.Source: §2.3.1 · pp. 2–3

2.3.2. Degree distributions.

• A node's degree counts its links to other nodes, while its weighted degree sums transaction counts assigned as link weights.The degree includes a self-link when a loop occurs.Source: §2.3.2 · p. 3

2.3.3. Distance.

• Average distance is the average shortest-path length across node pairs and is considered together with clustering when assessing small-world structure.Shortest distances are calculated using breadth-first search.Source: §2.3.3 · p. 3

2.3.4. Clustering coefficient.

• The clustering coefficient measures how often connected neighbors are also connected, using triangles relative to connected triplets.A triangle contributes three connected triplets; in the Ethereum setting, it represents three accounts with transactions among each pair.Source: §2.3.4 · p. 3

2.3.5. Small worlds.

• A network is classified as small-world when its clustering is significantly higher than that of a same-sized random graph while average distance remains small.The random-graph comparison uses clustering coefficient and average distance; σ significantly above 1 indicates a small world.Source: §2.3.5 · p. 3

3. The Ethereum Blockchain as a Network

• Ethereum accounts are network nodes and transactions between them are links that can be weighted by transaction count or transferred currency.Source: §3 · p. 3
• 28,867 active accounts and 32,800 links make up the analyzed approximately one-hour network, where several nodes have many transactions and most have a single entering or exiting link.The network covers approximately 240 blocks.Source: §3 · p. 3, Figure 1 · p. 4

3.1. EtherNet Galaxy: a Software for Blockchain Analysis

• EtherNet Galaxy retrieves block data through Infura, extracts transactions with web3-eth into Pajek-format networks, and analyzes them with NetworkX.The reported analysis used a prototype; the software was under development.Source: §3.1 · pp. 3–4

4. Results

• As block coverage widens, metrics increase, clustering remains low, and the main component contains about 90% of nodes in the largest network.The single-block network is sparse, has no triangles, and has relatively many components compared with its node count.Source: §4 · pp. 4–5

4.1. Degree Distribution

• Most nodes remain degree 1 as block coverage grows, while higher-degree nodes become more common and the long tail suggests a power law.The one-block network is simple, and its degree distribution is consistent with few accounts participating in more than one transaction per block.Source: §4.1 · p. 5, Figure 5 · p. 6, Figure 6 · p. 6

4.2. Small World Phenomenon

• The networks are not small worlds: clustering is almost zero, and the 10^2-block network has diameter 23.Although σ is very high for the 10^3-block network, the authors attribute that to a numerical outcome rather than evidence of a small world.Source: §4.2 · p. 6, Table 2 · p. 7, Table 3 · p. 7

4.3. Metrics at Different Snapshots

• Across snapshots, node and interaction counts generally grow over time, with a spike at block 5,000,000.The 10,000-block-interval results show an analogous trend to the 1,000-block intervals.Source: §4.3 · pp. 6–7, Figure 11 · p. 8
• The block-5,000,000 snapshot coincides with an Ether price spike; the authors suggest higher currency value may accompany greater activity, while clustering shows no specific trend.All snapshot networks have low average clustering, similar to values in earlier analyses.Source: §4.3 · pp. 7, 9, Figure 12 · p. 9

4.4. Miners Distribution

• Among roughly 180,000 blocks, six miners mined over 10,000 blocks each, and one mined 47,193.The authors suggest these high-volume nodes are probably mining pools.Source: §4.4 · p. 9

• Varying the number of blocks changes the temporal range, transaction count, and size of the Ethereum transaction network.Source: §5 · p. 9
• Wider networks are more likely to contain hubs, indicating that some nodes are more active in the blockchain.Source: §5 · p. 9
• Using subsets of subsequent blocks allows the analysis to track how blockchain use changes over time.Source: §5 · p. 9
• Although accounts are pseudonymous, a hub that is not a popular smart contract and repeatedly uses the same account may be easier to de-anonymize.Source: §5 · p. 9