Lightning Network Empirical Insights

• The paper demonstrates that LN exhibits a core–periphery topology where the top 10% nodes control over 80% of liquidity, raising centralization concerns.
• The paper reveals that Dijkstra’s algorithm outperforms BMSSP in real LN snapshots, though dynamic liquidity and convergence delays still challenge routing efficiency.
• The paper highlights that fee dynamics favor central hubs and expose privacy risks while liquidity imbalances and rebalancing challenges impact overall network performance.

The Lightning Network (LN) is an off-chain payment channel network designed to scale Bitcoin transactions by facilitating rapid, low-fee, multi-hop payments among participants. The architecture, relying on a dynamic, sparse graph of bidirectional payment channels with liquidity constraints, incentivizes strategic routing, fee setting, and network positioning, while raising acute challenges in economic rationality, performance, decentralization, reliability, and privacy. A large body of empirical work leverages public network snapshots, topology logging, payment simulation, and statistical methodologies to analyze operational metrics and network evolution.

1. Topological Structure and Centralization

LN evolves as a sparse, connected, undirected multigraph where nodes represent participants and edges represent payment channels with designated capacities and fee policies. Several empirical studies observe heavy-tailed degree and capacity distributions (power-law exponents α ∈ [2,3]), persistent sparsification over time (link density ρ ∼ c N^{-1}), and robust core–periphery (hub-and-spoke) structure, with topological properties summarized in Table 1 (Feichtinger et al., 2024, Lin et al., 2020, Martinazzi, 2019).

Property	Empirical Value (2018–2023)	Source
Node count	5,000 – 20,000	(Feichtinger et al., 2024)
Channel count	30,000 – 150,000	(Feichtinger et al., 2024)
Mean degree ⟨k⟩	7 – 11	(Feichtinger et al., 2024)
Largest component size	>99% of nodes	(Feichtinger et al., 2024)
Diameter	7 – 9	(Feichtinger et al., 2024)
Avg. Gini (strength)	0.9 (last snapshot)	(Lin et al., 2020)
Top 10% nodes (BTC)	~80% of total capacity	(Lin et al., 2020)

The combination of low average degree, short diameter, and high Gini indices in node strength or centrality reflects a robust yet centralized backbone; >80% of routing liquidity is concentrated among a small fraction of nodes. The UBCM random-graph baseline fails to capture the degree of observed hub dominance, indicating a topological evolution toward core–periphery arrangements (Lin et al., 2020).

Centrality analyses quantify the increasing concentration of flow through high-betweenness nodes: by 2021, the top 10% of nodes controlled 82% of shortest-path volume, up from 77% in early 2019; Gini betweenness rose from ≈0.72 to ≈0.84 (Zabka et al., 2022). This skew, reinforced by autopilot heuristics and economic incentives to favor well-connected peers, reduces effective decentralization and exacerbates single-point vulnerabilities.

2. Routing Performance and Algorithmic Evaluation

Payment pathfinding is generally modeled as a single-source shortest-path problem in a directed, weighted graph, where each path’s cost is determined by per-edge base and proportional fees, and the feasibility is subject to dynamic capacity constraints. Dijkstra’s algorithm, implemented via a binary heap, remains the default in all leading LN node software, with $O(m+n \log n)$ worst-case runtime (Valko et al., 16 Sep 2025).

Recent theoretical advances (BMSSP with $O(m \log^{2/3} n)$ runtime) have motivated empirical benchmarking on real LN snapshots (4,000–16,000 nodes, 30,000–78,000 channels). Valko et al. implemented both algorithms in Rust with standardized data representation and simulation protocols. Across all tested conditions, Dijkstra’s wall-clock runtime per single-source invocation was consistently ~0.8× that of BMSSP, with lower variance (Valko et al., 16 Sep 2025). The expected asymptotic advantage of BMSSP was offset by practical overheads: recursive stack growth, amortized memory indirection, and subroutine dispatches. Both algorithms displayed nearly linear scaling with respect to node count and edge count. The study concludes that Dijkstra’s implementation is empirically superior at current LN scales, though future architectural and low-level optimizations could tip the balance on larger graphs.

3. Economic Incentives, Routing Revenue, and Fee Dynamics

Transaction fee revenue in LN depends on the routing algorithm, network position, channel capacity, and fee setting. Multiple studies report that centralization or "rich-get-richer" dynamics dominate the network’s fee economy (Carotti et al., 2023, Beres et al., 2019). For a capacity-proportional traffic model, the top bucket of nodes by total liquidity earns R(u) (revenue per staked satoshi) 3–5× greater than lower buckets. Correlations between revenue and structural centrality are high: Spearman ρ(R, capacity) ~0.5–0.7; with BC-weighted paths, ρ can climb to ~0.8 under fee- or capacity-aware routing (Carotti et al., 2023).

Peripheral nodes (low liquidity, low degree) have effectively zero average revenue per satoshi. Rational adaptation scenarios demonstrate that when nodes can only change fee policy, network-wide mean fees increase over time, favoring entrenched hubs. In contrast, neighbor rewiring by high-capacity nodes leads to flattened degree distribution and declining mean fees, promoting competitiveness and partial de-centralization (Carotti et al., 2023).

Simulations with fixed-size payments (10,000 satoshis) and realistic routing and choice models show large routing nodes can, by imitating the channel structure and fee policy of more successful peers, realize up to a 50% uplift in fee revenue (Carotti et al., 2023).

Fee profitability remains limited: historical studies estimate even the most active routers receive daily revenues well below the threshold for positive annual RoI unless channels or traffic volumes increase by an order of magnitude or fees rise substantially (Beres et al., 2019). Under a competitive fee equilibrium (routing nodes charging up to the price gap to next-best paths), only a handful of operators break even.

4. Availability, Reliability, and Routing Success

Payment success is not guaranteed due to dynamic liquidity constraints, node churn, and stale or incomplete network state. Active probing across the network reveals a strong inverse relationship between payment amount and success rate:

Payment Volume (USD)	S(v) Success [%]	R(v) Reach [%]	Nodes Reachable
0.01	71.92	35.24	1630
1.00	57.82	35.19	1628
5.00	44.06	25.66	1187
10.00	44.15	33.72	1560
50.00	30.93	9.22	459
100.00	17.30	4.82	223

Even for cent-scale payments, only about 35% of nodes are reachable. Channel-funding failures (insufficient one-way liquidity) are the dominant transient error. Node lifetime is generally high on the scale of days to weeks; short-term churn is low, but network directory information is inaccurate—>60% of IPv4 addresses and ~30% of .onion addresses are stale (Waugh et al., 2020).

A large fraction of public nodes are hosted on cloud or backbone ASes (Google, DigitalOcean, Cogent, Comcast, OVH), indicating a reliance on centralized infrastructure providers.

The routing convergence delay (network-wide propagation of new channel/fee data) is a further limiting factor: median convergence of 5–10 minutes is typical in LND’s default configuration, with keep-alive updates consuming nearly half the gossip bandwidth. Payment-failure rate scales linearly with the convergence delay; parameter or protocol optimizations (batch size, interval, set-reconciliation) can cut delays by 50–95%, improving routing reliability (Gögge et al., 2022).

5. Channel Rebalancing, Liquidity Optimization, and Dynamic Network Algorithms

A key challenge in PCNs is persistent imbalance: as payments flow, liquidity accumulates asymmetrically, undermining routability. Pickhardt and Nowostawski define node-level and network-level imbalance metrics, formalize rebalancing as a Gini-minimization problem over private channel balances, and demonstrate a greedy, cycle-based heuristic enabling each node to improve local balance using only limited local knowledge (Pickhardt et al., 2019). In simulation, this protocol reduces median node imbalance from 0.50 to 0.15 (KS distance=0.74), and boosts the 1-Satoshi payment success rate from 11.2% (imabalanced) to 98.3% (after rebalancing). All four tested cycle-selection strategies (search depth ≤5, friend-of-a-friend, mpp) yield similar global improvement. Empirically, fees incurred and earned during mutual rebalancing events net to ≃0 per node, motivating the recommendation to drop rebalancing fees in practice.

6. Privacy, Anonymity, and Information Leakage

Despite onion routing, LN’s privacy guarantees are limited by topological characteristics, fee schedules, and protocol-level observability. Several attack vectors exist:

• Balance probing: By combining probing payments and binary search, an attacker can determine the exact balance of >55% of public channels without relying on error-message side-channels (Kappos et al., 2020).
• On-path sender/receiver inference: The short average path length (~2.8) and high hub-concentration lead to 15–83% (scenario-dependent) chance that a non-hub intermediary trivially learns sender or receiver on 2-hop (single-intermediary) routes. 16–34% of payments are 2-hop in practice.
• Snapshot-differencing (off-path inference): Observers with access to periodic network states can reconstruct 67–74% of individual payments with 95% precision (at 30s granularity) (Kappos et al., 2020).
• Private channel recognition: On-chain heuristics and peeling-chain analysis enable identification of ~27,000 previously unadvertised private channels, with both endpoints identified in 7.5% of cases.

Empirical studies confirm that increased path length (forced multi-hop) raises plausible-deniability sets, at minor fee increase (~20%; e.g., from 2- to 6-hop path, cost rises from 52 to 60 satoshis) (Beres et al., 2019). Countermeasures include dummy traffic, channel-balance blinding, more uniform topologies, and enhanced HTLC constructions, but no deployed mechanism currently eliminates these weaknesses.

7. Resilience, Attachment Strategies, and Network Evolution

Resilience analysis demonstrates that LN is robust to random failures (random node removal up to 200 nodes leaves >90% reachability), but extremely vulnerable to targeted attacks against high-centrality nodes or minimum-cut removal. Removing the top 90–120 nodes by betweenness or degree typically cuts payment success by >50%; minimum cut strategies are even more efficient, with similar disruption using only 5% of nodes (Rohrer et al., 2019, Lin et al., 2020). Channel exhaustion and node isolation attacks, empirically validated, can disrupt routing and partition the network.

The empirical impact of attachment strategies indicates a clear decentralization–performance trade-off (Lange et al., 2021). Preferential (highest-degree, betweenness) strategies maximize immediate routing success and fee revenue for joiners, but exacerbate centralization and structural vulnerability. Center/median-based or randomized attachments minimize long-term network diameter and centralization (Gini to 0.29–0.32), at only a moderate cost to individual revenue. Simulation over 5,000 nodes shows k-center rapidly yields full connectivity, lower average fees, and higher resilience than hub-centric strategies.

• (Valko et al., 16 Sep 2025) Valko et al., "Outperforming Dijkstra on Sparse Graphs: The Lightning Network Use Case"
• (Carotti et al., 2023) "Rational Economic Behaviours in the Bitcoin Lightning Network"
• (Lin et al., 2020) "Lightning Network: a second path towards centralisation of the Bitcoin economy"
• (Waugh et al., 2020) "An empirical study of availability and reliability properties of the Bitcoin Lightning Network"
• (Pickhardt et al., 2019) "Imbalance measure and proactive channel rebalancing algorithm for the Lightning Network"
• (Feichtinger et al., 2024) "Benchmarking GNNs Using Lightning Network Data"
• (Lange et al., 2021) "On the Impact of Attachment Strategies for Payment Channel Networks"
• (Beres et al., 2019) "A Cryptoeconomic Traffic Analysis of Bitcoin's Lightning Network"
• (Gögge et al., 2022) "On the Routing Convergence Delay in the Lightning Network"
• (Kappos et al., 2020) "An Empirical Analysis of Privacy in the Lightning Network"
• (Martinazzi, 2019) "The evolution of Lightning Network's Topology during its first year and the influence over its core values"
• (Zabka et al., 2022) "A Centrality Analysis of the Lightning Network"
• (Rohrer et al., 2019) "Discharged Payment Channels: Quantifying the Lightning Network's Resilience to Topology-Based Attacks"