- The paper reveals that miner nodes, identified via graph theory, form a dense, high-centrality core that excludes peripheral full nodes from efficient transaction paths.
- It employs empirical data and simulations to show that both BTC and BSV networks exhibit power-law, small-world properties dominated by resource-rich miner hubs.
- Findings suggest that network monitoring and transaction relay should prioritize miner connectivity over counting non-mining full nodes for reliable system performance.
This paper (2506.14197) presents a formal analysis of the Bitcoin (BTC) and Bitcoin Satoshi Vision (BSV) network structures using complex graph theory to demonstrate that non-mining full nodes are functionally redundant in transaction and block propagation topologies. The central argument is that the network topology is dominated by a densely interconnected clique of miner nodes, while non-mining full nodes reside on the periphery and are excluded from critical propagation paths.
The research employs several key concepts from network science:
- Scale-free networks: The network exhibits a power-law degree distribution, where a small number of nodes (miners) have a disproportionately large number of connections, acting as hubs.
- Small-world properties: The miner subgraph shows low average shortest path lengths and high clustering, indicating efficient communication within this core.
- Fitness-driven preferential attachment: Nodes with higher fitness (e.g., bandwidth, uptime, low latency) attract more connections over time, reinforcing the dominance of resource-rich miners.
The paper contrasts the idealized vision of a flat, egalitarian peer-to-peer network with the observed reality, which is a hierarchical structure where miner connectivity determines the effective topology for transaction and block relay.
The methodology relies on both empirical data and simulations:
- Empirical Data: Network snapshots, latency measurements, and peer lists from live BTC and BSV networks, drawing on previous studies [e.g., (2002.03771, Gencer et al., 2018)]. This data is used to infer the directed adjacency matrix of the propagation graph, weighting edges by factors like inverse latency and uptime.
- Simulation Environment: A discrete-event simulation calibrated with empirical parameters (degree distribution, latency, churn) is used to model transaction propagation and graph evolution. This allows for controlled experiments and observation of emergent topological properties.
- Graph Analysis: Standard graph theory metrics are applied, including:
- Degree distribution analysis to identify scale-free properties.
- Centrality measures (betweenness, closeness, eigenvector centrality, PageRank) to quantify node influence.
- Spectral analysis of the adjacency and Laplacian matrices to understand propagation dynamics and connectivity robustness.
- k-core decomposition to identify the core structure of the network.
- Shortest path computation to analyze transaction propagation routes.
- Live-Network Validation: Targeted transaction injections from peripheral nodes in live networks are used to measure propagation paths and latencies, validating the simulation results and empirical topology inference.
Key findings supporting the paper's thesis include:
- Network Metrics: Miner nodes consistently show significantly higher centrality scores (eigenvector, betweenness) and form a core with high clustering and low diameter compared to non-mining full nodes.
- Degree Distributions: Both BTC and BSV networks exhibit power-law degree distributions with exponents suggesting pronounced hub formation. Miner nodes occupy the heavy tail of this distribution.
- Graph Topology: Visualizations and structural analysis (like k-core decomposition) consistently show a dense, interconnected miner clique and a sparsely connected periphery of full nodes.
- Path Exclusion: Formal analysis and empirical observation show that non-mining full nodes are consistently excluded from the shortest or most efficient transaction propagation paths to miners. Transactions typically route directly from users to miners or entirely within the miner network.
- Seed-Based Connectivity and Miner Link Persistence: The network bootstrap process (DNS seeds, hardcoded peers) biases initial connections towards reliable, high-uptime nodes, which are predominantly miners. Miner-to-miner links are shown to be highly persistent, forming a stable backbone, unlike transient full node connections.
The theoretical analysis formalizes these observations through lemmas and propositions, demonstrating that:
- Under fitness-based preferential attachment, central nodes acquire disproportionately more links.
- The principal eigenvector of the adjacency matrix, representing propagation influence, concentrates weight exclusively on miner nodes.
- Non-mining full nodes fall outside the higher k-cores of the network, indicating their lack of structural redundancy.
- Propagation paths converge towards the miner-only subgraph due to latency optimization and peering policies.
Practical Implications for Implementation and Application:
The paper's findings have significant practical implications for anyone building on, monitoring, or analyzing Bitcoin:
- Network Monitoring and Analysis: Simply counting total full nodes is a misleading metric for network decentralization or health. Practitioners should focus on analyzing the connectivity and centrality of miner nodes and large relay services. Tools should be adapted to identify and track these core entities and their interconnections.
- Transaction Relay Optimization: Applications needing fast and reliable transaction propagation (e.g., exchanges, payment processors) should prioritize establishing direct, low-latency connections to multiple major mining pools or known miner relay networks. Relying on propagation through typical full nodes is inefficient and unreliable.
- Wallet and Node Software Design: For non-mining nodes, the primary function is validation, not active propagation contribution. Software design should reflect this reality. While receiving block and transaction broadcasts is necessary for validation, these nodes are effectively clients consuming data from the miner backbone.
- Simulating Bitcoin Network Behavior: Realistic simulations must incorporate the observed core-periphery structure, preferential attachment, and latency weighting. Simple random graph models or homogeneous peer assumptions will fail to capture the true propagation dynamics.
- Understanding System Security and Resilience: The core-periphery structure implies that the network's resilience against disruption of propagation depends heavily on the robustness and connectivity of the miner clique, not the sheer number of peripheral nodes. Attack surfaces related to transaction propagation would likely target the miner core or critical relay hubs.
- BSV vs. BTC: Despite differing design philosophies post-fork (BSV allowing larger blocks, BTC maintaining small blocks), the fundamental network topology remains miner-centric in both, driven by the economic incentives of mining and the technical realities of large-scale distributed systems. The paper argues the BSV model aligns better with the original white paper's focus on miner-led propagation but still exhibits core dominance.
In summary, the paper provides strong evidence, both empirical and theoretical, that the concept of full node count as a measure of Bitcoin's decentralization or resilience is unfounded. The network operates as a miner-dominated system where propagation critical functions are confined to a highly connected core, rendering non-mining full nodes structurally peripheral and functionally redundant.
