Concentration Within Distribution: Unmasking Bitcoin's Structural Centralization Through Network Science

TL;DR

This work addresses the paradox of Bitcoin's decentralization by uncovering emergent concentration in the Bitcoin User Network (BUN) through mesoscopic network analysis of full-node blockchain data (2011–2025). It advances the methodology by incorporating direction-sensitive centralities (PageRank, HITS) alongside traditional connected-component and assortativity analyses, revealing a persistent backbone and pronounced core-periphery structure. The study also pairs network insights with a high-frequency volatility analysis, showing that centralization patterns coexist with decreasing volatility magnitudes over time, while centrality inequality remains high. These findings suggest systemic importance and potential vulnerability in Bitcoin's emergent organizational structure, underscoring the need for refined clustering heuristics and risk assessment linked to external events.

Abstract

We construct the Bitcoin User Network (BUN) directly from raw blockchain data up to late 2025, which allows us to explore its mesoscopic properties and trace its temporal evolution. In particular, we analyze the structure of connected components and directed assortativity through the four variants of Newman's coefficient, implemented via custom algorithms and a dedicated database. Building on this, to characterize the distribution of structural influence, we introduce direction-sensitive centrality measures based on PageRank and HITS, which provide a complementary global analysis of the BUN and reveal a persistently unequal and increasingly core-periphery structure. In addition, we complement the structural analysis with a study of Bitcoin's price volatility using high-frequency market data. Overall, our results reveal a clear pattern of concentration within distribution: although the protocol is decentralized by design, the emergent user network evolves toward an asymmetric mesoscopic structure that indicates the existence of a few large-scale connected components that function as the critical backbone of the system.

Figures (14)

• Figure 1: Weekly number of Bitcoin transactions from 2011 to 2025, showing long-term growth from under 1 million to peaks near 5 million transactions per week.
• Figure 2: Snapshots of the BUN at different time intervals. (a) Early 2011 (week 104), showing initial network formation. (b) Ten weeks later (week 114), illustrating the rapid expansion of the network
• Figure 3: Distribution of Bitcoin transactions by number of inputs ($v_\text{in}$) and outputs ($v_\text{out}$) during week 700. "1-1" indicates transactions with one input ($v_\text{in}=1$) and one output ($v_\text{out}=1$); "1-2" indicates $v_\text{in}=1$ and $v_\text{out}=2$; "1-3" indicates $v_\text{in}=1$ and $v_\text{out}=3$; and "other" represents all other combinations of $v_\text{in}$ and $v_\text{out}$.
• Figure 4: Representation of transactions and user groupings of Table \ref{['TableAddress']}. The arrows indicate transactions between addresses, while the colored blocks correspond to users grouped according to Table \ref{['TableAddress']}. User 2 (U2) is shown in red, user 4 (U4) in green, and user 1 (U1) in blue. The dashed line indicates the grouping of addresses that also belong to user 1. The numbers inside the blocks represent, as an example, arbitrary amounts of BTC transferred between transactions.
• Figure 5: Representation of the Bitcoin User Network (BUN) elements, where users $i$ and $j$ are modeled as nodes, and each edge $ij$ denotes a value transfer (transaction $ij$) between them.