TOPOLOGY EXPLORER

Lightning Network Topology

Scale-free Networks, Centralization Analysis, Hub Failure Simulation, and Graph Theory of the Lightning Network

Scale-Free Barabási–Albert Hub Failure Gini Coefficient Betweenness Centrality Force-Directed Layout
Section 1

What Kind of Network is Lightning?

Lightning Network is not a random graph — it exhibits a power-law degree distribution, making it a classic scale-free network. A handful of high-degree hub nodes dominate, while the vast majority have very few channels.

~2.1
Power-law exponent γ
60%
Nodes with ≤3 channels
30%
Capacity by top 10 nodes
2.7
Avg path length (hops)
~7
Average node degree
Key finding (Seres et al. 2020): LN degree distribution follows a power law P(k) ∝ k−γ with γ ≈ 2.1 — the same structural regime as the internet, airline routes, and social networks.

Erdős–Rényi Random Graph

Uniform degree distribution — each node has roughly the same number of connections. Resilient to targeted attacks but no natural hubs.

Scale-Free Graph (Lightning Network)

Hub-and-spoke topology — few massive hubs, many leaf nodes. Efficient routing but fragile to hub removal.

Degree Distribution Comparison

P(k) — Probability of degree k (log scale)
Erdős–Rényi (random)
Scale-Free (LN-like)
Section 2 — Main Feature

Interactive Network Simulator

A Barabási–Albert scale-free network generated in pure JavaScript using preferential attachment. Click nodes to explore their connections and statistics.

Node color:
Hub (≥15 channels)
Mid (5–14)
Leaf (1–4)

Node Info

Degree—
Capacity (BTC)—
Betweenness—
Category—
Click another node or background to dismiss
Section 3

Hub Failure Simulation

Scale-free networks are resilient to random failures but fragile to targeted attacks on hubs. This is the fundamental security trade-off of the Lightning Network topology.

⚠️ Critical insight: Removing just the top 5 hub nodes can disconnect ~30% of the network. Random node failures have negligible impact until 40%+ of nodes are removed.
Mode:

Live Network Metrics

100%
LCC Size
2.7
Avg Path (hops)
0
Isolated Nodes
Largest Connected Component vs Nodes Removed
Targeted (scale-free)
Random (scale-free)
Random (ER baseline)
Section 4

Centralization Metrics Dashboard

Multiple complementary metrics quantify how concentrated the Lightning Network has become. High Gini coefficient, top-N concentration, and betweenness centrality all point to growing centralization.

Lorenz Curve — Capacity Inequality

Cumulative nodes (X) vs cumulative capacity (Y)
LN estimated Gini ≈ 0.88 — comparable to global wealth inequality. The top 1% of nodes control ~30% of all capacity.

Top-N Capacity Concentration

% of total network capacity controlled by top N%

Eccentricity / Diameter Impact

Average path length increases as hubs are removed:

Betweenness Centrality

Betweenness centrality measures how many shortest paths pass through each node. High-betweenness nodes are critical routing hubs — if they fail, many payments must find alternative routes.

Rohrer et al.: Betweenness centrality is a better predictor of routing impact than degree alone. A node with moderate degree but high betweenness is more critical than a high-degree leaf-cluster node.
Section 5

Routing Efficiency vs Topology

The topology of the network directly determines routing success rates, fees, and path lengths. Compare three different topology regimes.

CURRENT LN (SCALE-FREE)
85%
Success Rate
150
Avg Fee (sats)
2.7
Avg Hops
UNIFORM RANDOM (ER GRAPH)
60%
Success Rate
280
Avg Fee (sats)
4.2
Avg Hops
PERFECT MESH
99%
Success Rate
50
Avg Fee (sats)
1.0
Avg Hops

Note on Perfect Mesh

While a complete mesh offers near-perfect routing, it requires O(N²) on-chain transactions to open all channels. For 10,000 nodes, that's ~50 million channels — economically and technically impractical.

Radar Comparison — 5 Dimensions

Scale-Free (LN)
ER Random
Perfect Mesh
Section 6

Historical Network Growth (2018–2025)

The Lightning Network grew from 75 nodes in early 2018 to a peak of ~16,000 nodes in 2022, then stabilized. Capacity continued growing even as node count declined.

Year: 2018
Nodes over time
Channels over time
Total capacity (BTC) over time

Key Events

JAN 2018
Lightning Network mainnet launch — first 75 nodes
2019–2020
ACINQ Phoenix wallet launch — major usability improvement
SEP 2021
El Salvador adopts Bitcoin as legal tender — Chivo wallet drives LN adoption
2022 PEAK
~16,000 nodes, 75,000 channels — network peak size, then consolidation
2023
Node count declines as hobbyist operators close channels; capacity grows
2024–2025
LSPs (Lightning Service Providers) increasingly dominate topology
Section 7

Research Insights & Key Papers

Empirical studies have quantified LN topology, centralization dynamics, and vulnerability profiles.

Seres et al. (2020) — Topological Analysis of Bitcoin's Lightning Network

FC 2020 / arXiv:1901.04972
First comprehensive study of LN topology using real snapshot data. Demonstrated power-law degree distribution, small-world properties, and rich-club phenomenon. Computed both unweighted (by channel count) and weighted (by capacity) versions.
🔑 LN degree distribution follows P(k) ∝ k−2.1. Network diameter ~6 hops maximum, average path ~2.7. Rich-club coefficient confirms hubs preferentially connect to other hubs. Betweenness centrality heavily concentrated in 10–20 nodes.

Lin et al. (2020) — Measuring Decentralization in Bitcoin's Lightning Network

IEEE ICBC 2020
Longitudinal study tracking centralization over time. Shows that despite growing node count, centralization metrics (Gini, Nakamoto coefficient, HHI) have been increasing — driven by preferential attachment dynamics.
🔑 Nakamoto coefficient (min nodes needed to control 50% capacity): dropped from ~12 in 2018 to ~5 in 2020. Gini coefficient for capacity: 0.85–0.92. Trend toward more centralization despite more nodes.

Rohrer et al. — Discharged Payment Channels: Quantifying the Lightning Network's Resilience

IEEE Blockchain 2019
Systematic node removal experiments on real LN snapshots. Compared random, degree-based, and betweenness-based removal strategies. Found betweenness-targeted removal most disruptive.
🔑 Removing top-k% nodes by betweenness: LCC collapses at k≈5–8%. By degree: similar collapse at k≈10–15%. Random removal: network survives until k≈40%. Betweenness centrality better predicts routing impact than degree.

Pickhardt & Richter (2021) — Optimally Reliable & Cheap Payment Flows on the Lightning Network

ACM AFT 2021 / arXiv:2107.05322
Introduced minimum cost flow (MCF) framework for payment routing, showing that hub topology creates predictable liquidity concentration. Probabilistic models of channel liquidity enable better path selection.
🔑 Hub concentration means most liquidity is predictably located. MCF routing achieves 2–10× better success rates than shortest-path heuristics. Hub-and-spoke topology actually aids MCF optimization.
Section 8

Proposed Solutions to Centralization

Researchers and protocol designers have proposed several approaches to reduce centralization and improve topological resilience.

Channel Factories

PROPOSAL / RESEARCH

Create many channels between multiple parties with a single on-chain transaction. This dramatically reduces the cost of opening channels, enabling more meshed topologies without prohibitive on-chain fees.

Ref: Burchert et al. (2018) "Scalable Funding of Bitcoin Micropayment Channel Networks"

Trampoline Routing

DEPLOYED (Eclair/Phoenix)

Allows mobile nodes to route through intermediate "trampoline" nodes without maintaining full network knowledge. Reduces dependency on mega-hubs for route discovery while keeping routing private.

Ref: BOLT-style proposal by Bastien Teinturier (ACINQ), deployed in Phoenix wallet

Flare Routing Protocol

RESEARCH

Hybrid routing where each node maintains local topology information about its neighborhood and uses beacons (well-connected nodes) for distant routing. Reduces need to connect to all hubs.

Ref: Prihodko et al. (2016) "Flare: An Approach to Routing in Lightning Network"

Fee Policy Reform

RESEARCH / DEBATE

Designing fee mechanisms that automatically discourage excessive centralization — e.g., progressive fees that scale nonlinearly with node size, or reputation systems that reward decentralized topologies.

Ref: Pickhardt et al. routing economics papers; ongoing LN dev mailing list discussion

Geographic & ISP Diversity

OPERATIONAL CONCERN

Many LN nodes are co-located in a few cloud providers (AWS, Hetzner). Encouraging geographic distribution and multi-provider diversity improves resilience against infrastructure-level failures and censorship.

Ref: Analyzed in Seres et al. and Grundmann et al. (2021) network measurement studies

LSP Competition & Regulation

EMERGING

Lightning Service Providers (LSPs) are becoming dominant routing hubs. Ensuring interoperability via LSPS0-2 standards and competitive LSP markets may be the most practical path to maintaining decentralization.

Ref: LSP Specs (LSPS0, LSPS1, LSPS2); River Financial annual reports 2022-2023