The evolving topology of the Lightning Network: Centralization, efficiency, robustness, synchronization, and anonymity

Autoři: Stefano Martinazzi aff001;  Andrea Flori aff001
Působiště autorů: Politecnico di Milano, Department of Management, Economics and Industrial Engineering, Milan, Italy aff001
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article


The Lightning Network (LN) was released on Bitcoin’s mainnet in January 2018 as a solution to favor scalability. This work analyses the evolution of the LN during its first year of existence in order to assess its impact over some of the core fundamentals of Bitcoin, such as: node centralization, resilience against attacks and disruptions, anonymity of users, autonomous coordination of its members. Using a network theory approach, we find that the LN represents a centralized configuration with few highly active nodes playing as hubs in that system. We show that the removal of these central nodes is likely to generate a remarkable drop in the LN’s efficiency, while the network appears robust to random disruptions. In addition, we observe that improvements in efficiency during the sample period are primarily due to the increase in the capacity installed on the channels, while nodes’ synchronization does not emerge as a distinctive feature of the LN. Finally, the analysis of the structure of the network suggests a good preservation of nodes’ identity against attackers with prior knowledge about topological characteristics of their targets, but also that LN is probably weak against attackers that are within the system.

Klíčová slova:

Centrality – Eigenvalues – Network analysis – Network resilience – Operator theory – Payment – Scale-free networks – Algebraic topology


1. Croman K, Decker C, Eyal I, Gencer AE, Juels A, Kosba A, et al. On scaling decentralized blockchains. In: International Conference on Financial Cryptography and Data Security 2016 Feb 26; Christ Church, Barbados. Berlin, Heidelberg: Springer; 2016. p. 106–125.

2. Vukolic M. The Quest for Scalable Blockchain Fabric Proof-of-Work vs. BFT Replication In: Camenisch J, Kesdogan D, editors. Open Problems in Network Security. iNetSec 2015. Lecture Notes in Computer Science; 2015 Oct 29; Zurich, Switzerland. Springer, Cham; 2016. p.112–125.

3. Lee TB. Bitcoin’s transaction fee crisis is over-for now, 2018 Feb 20 [Cited the 05 April 2019]. In Arsthecnica [internet]. New York: Condé Nast Inc. c2018 -. [about 5 screens] Available from:

4. Polasik M, Piotrowska AI, Wisniewski TP, Kotkowski R, Lightfoot G. Price fluctuations and the use of bitcoin: An empirical inquiry. International Journal of Electronic Commerce. 2015; 20(1): 9–49. doi: 10.1080/10864415.2016.1061413

5. Corbet S, Lucey B, Urquhart A, Yarovaya L. Cryptocurrencies as a financial asset: A systematic analysis. International Review of Financial Analysis. 2019; 62: 182–199. doi: 10.1016/j.irfa.2018.09.003

6. Flori A. Cryptocurrencies in Finance: Review and Applications. International Journal of Theoretical and Applied Finance (IJTAF). 2019; 22(05): 1–22.

7. Poon J, Dryja T. The Bitcoin Lightning Network: Scalable Off-Chain. DRAFT Version 2016 [cited 05 April 2019]. Available from:

8. Conoscenti M, Vetrò A, De Martin J. The CLoTH Simulator for HTLC Payment Networks with Introductory Lightning Network Performance Results. Information. 2018;9(9): 223. doi: 10.3390/info9090223

9. Decker C, and Roger W. A Fast and Scalable Payment Network with Bitcoin Duplex Micropayment Channels. In: Pelc A, Schwarzmann A, editors. Stabilization, Safety, and Security of Distributed Systems. 2015 Aug 18-21;Edmonton, Alberta, Canada. Springer, Cham; 2015. p. 3–18.

10. Aiken S. Lightning Network: 27 concerns about UX and centralization. 2018 May 22 [Cited the 05 April 2019]. In: Medium [Internet]. San Francisco: A Medium Company. c2018-. [about 51 screens] Available from:

11. Kondor D, Pósfai M, Csabai I, Vattay G. Do the rich get richer? An empirical analysis of the Bitcoin transaction network. PLOS ONE. 2014;9(2): e86197. doi: 10.1371/journal.pone.0086197 24505257

12. Liang J, Li L, Zeng D. Evolutionary dynamics of cryptocurrency transaction networks: An empirical study. PLOS ONE. 2018;13(8): e0202202. doi: 10.1371/journal.pone.0202202 30118501

13. Topirceanu A, Udrescu M, Marculescu R. Weighted Betweenness Preferential Attachment: A New Mechanism Explaining Social Network Formation and Evolution. Scientific Reports. 2018;8(1): 10871. doi: 10.1038/s41598-018-29224-w 30022079

14. Editorial Staff Lightning Strikes, But Select Hubs Dominate Network Funds. 25 June 2018 [Cited the 05 April 2019]. In Diar [internet]. Nicosia: Diar Ltd. c2018-. [about 2 screens] Available from:

15. Leung C, Chau F. Weighted Assortative And Disassortative Networks Model. Physica A: Statistical Mechanics and its Applications. 2007;378(2): 591–602. doi: 10.1016/j.physa.2006.12.022

16. Chopra SS, Dillon D, Bilec MM, Khanna V. A network-based framework for assessing infrastructure resilience: a case study of the London metro system. Journal of The Royal Society Interface. 2016;13.118: 20160113. doi: 10.1098/rsif.2016.0113

17. Bagler G. Analysis of the Airport Network of India as a complex weighted network. Physica A: Statistical Mechanics and its Applications. 2008;387(12): 2972–2980. doi: 10.1016/j.physa.2008.01.077

18. Newman Mark EJ. The structure and function of complex networks. SIAM Review. 2003;45.2: 167–256. doi: 10.1137/S003614450342480

19. Jung WS, Chae S, Yang JS, Moon HT Characteristics of the Korean stock market correlations. Physica A: Statistical Mechanics and its Applications. 2016;361(1): 263–271. doi: 10.1016/j.physa.2005.06.081

20. Li W, Cai X. Empirical analysis of a scale-free railway network in China. Physica A: Statistical Mechanics and its Applications. 2007;382(2): 693–703. doi: 10.1016/j.physa.2007.04.031

21. Nacher JC, Hayashida M, Akutsu T. Protein domain networks: Scale-free mixing of positive and negative exponents. Physica A: Statistical Mechanics and its Applications. 2006;367: 538–552. doi: 10.1016/j.physa.2005.12.014

22. Wang WX, Wang BH, Hu B, Yan G, Ou Q. General dynamics of topology and traffic on weighted technological networks. Physical Review Letters. 2005;94(18): 188702. doi: 10.1103/PhysRevLett.94.188702 15904415

23. Barrat A, Barthélemy M, Vespignani A. Modeling the evolution of weighted networks. Physical Review E. 2004;70(6): 066149. doi: 10.1103/PhysRevE.70.066149

24. Clauset A, Shalizi CR, Newman MEJ. Power-law distributions in empirical data. SIAM Review. 2009;51(4): 661–703. doi: 10.1137/070710111

25. Barabasi Albert-László. Scale-free networks: a decade and beyond. Science. 2009;325.5939: 412–413. doi: 10.1126/science.1173299 19628854

26. Caldarelli G. Scale-free networks: complex webs in nature and technology. Oxford University Press; 2007.

27. Russell R. BOLT #2: Peer Protocol for Channel Management. 2016 Nov 15 [cited 21 February 2019]. In: GitHub [Internet]. San Francisco: GitHub Inc. c2016-. [about 25 screens] Available from:

28. Barabási AL, Albert R. Emergence of Scaling in Random Networks. Science. 1999;286(5439): 509–512. doi: 10.1126/science.286.5439.509 10521342

29. Simon HA. On a Class of Skew Distribution Functions. Biometrika. 1955;42(3-4): 425–440. doi: 10.2307/2333389

30. Latora V, Marchiori M. Economic Small-world behaviour in weighted networks. The European Physical Journal B. 2003;32(2): 249–263. doi: 10.1140/epjb/e2003-00095-5

31. Latora V, Marchiori M. Efficient behavior of small-world networks. Physical Review Letters. 2001;87(19): 198701. doi: 10.1103/PhysRevLett.87.198701 11690461

32. Doyle JC, Alderson DL, Li L, Low S, Roughan M, Shalunov S, et al. The “robust yet fragile” nature of the Internet. Proceedings of the National Academy of Sciences. 2005;102.41: 14497–14502. doi: 10.1073/pnas.0501426102

33. Albert R, Jeong H, Barabási AL. Error and attack tolerance of complex networks. Nature. 2000;406(6794): 378–381. doi: 10.1038/35019019 10935628

34. Bellingeri M, Cassi D. Robustness of weighted networks. Physica A: Statistical Mechanics and its Applications. 2018;489: 47–55. doi: 10.1016/j.physa.2017.07.020

35. Crucitti P, Latora V, Marchiori M, Rapisarda A. Efficiency of scale-free networks: error and attack tolerance. Physica A: Statistical Mechanics and its Applications. 2003;320: 622–642. doi: 10.1016/S0378-4371(02)01545-5

36. Korniss G, Huang R, Sreenivasan S, Szymanski BK. Optimizing synchronization, flow, and robustness in weighted complex networks. In: Thai MT, Panos PM, editors. Handbook of Optimization in Complex Networks. New York, NY: Springer-Verlag 2012. pp 31–96.

37. Arenas A, Díaz-Guilera A, Kurths J, Moreno Y, Zhou C. Synchronization in complex networks. Physics reports. 2008; 469(3): 93–153. doi: 10.1016/j.physrep.2008.09.002

38. Dörfler F, Chertkov M, Bullo F. Synchronization in complex oscillator networks and smart grids. Proceedings of the National Academy of Sciences. 2013; 110(6): 2005–2010. doi: 10.1073/pnas.1212134110

39. Kar S, Aldosari S, Moura JM. Topology for distributed inference on graphs. IEEE Transactions on Signal Processing. 2008; 56(6): 2609–2613. doi: 10.1109/TSP.2008.923536

40. Barahona M, Pecora LM. Synchronization in small-world systems. Physical Review Letters. 2002;89(5): 054101. doi: 10.1103/PhysRevLett.89.054101 12144443

41. Mitra C, Kurths J, Donner RV. Rewiring hierarchical scale-free networks: Influence on synchronizability and topology. EPL. 2006;119(3): 30002. doi: 10.1209/0295-5075/119/30002

42. Gupta V, Hassibi B, Murray RM. Stability analysis of stochastically varying formations of dynamic agents. In: 42nd IEEE International Conference on Decision and Control, Dec 9–12 2003; Maui, USA. IEEE, 2003. p. 504–509.

43. Atay FM, Bıyıkoğlu T, . Network synchronization: Spectral versus statistical properties. Physica D: Nonlinear Phenomena. 2006;224(1-2): 35–41. doi: 10.1016/j.physd.2006.09.018

44. Watanabe T, Masuda N. Enhancing the spectral gap of networks by node removal. Physical Review E. 2010;82(4): 046102. doi: 10.1103/PhysRevE.82.049901

45. Olfati-Saber R, Fax JA, Murray RM. Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE. 2007;95(1): 215–233. doi: 10.1109/JPROC.2006.887293

46. Jalili M. Enhancing synchronizability of diffusively coupled dynamical networks: a survey. IEEE transactions on neural networks and learning systems. 2013;24(7): 1009–1022. doi: 10.1109/TNNLS.2013.2250998 24808517

47. Hagberg A, Schult DA. Rewiring networks for synchronization. Chaos: An interdisciplinary journal of nonlinear science. 2008;18(3): 037105. doi: 10.1063/1.2975842

48. Chavez M. Hwang DU, Amann A, Boccaletti S. Synchronizing weighted complex networks. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2006;16(1): 015106. doi: 10.1063/1.2180467

49. Pecora LM. Synchronization of oscillators in complex networks. Pramana. 2008;70(6): 1175–1198. doi: 10.1007/s12043-008-0122-0

50. Kethineni S, Cao Y, . Use of bitcoin in darknet markets: Examining facilitative factors on bitcoin-related crimes. American Journal of Criminal Justice. 2018;43(2): 141–157. doi: 10.1007/s12103-017-9394-6

51. Reiter MK, Rubin AD. Crowds: Anonymity for web transactions. ACM transactions on information and system security (TISSEC). 1998;1(1): 66–92. doi: 10.1145/290163.290168

52. Diaz C, Seys S, Claessens J. Towards measuring anonymity. In: International Workshop on Privacy Enhancing Technologies, Apr 14–15 2002; San Francisco, USA. Springer, 2002. p. 54–68.

53. Sarfraz U, Alam M, Zeadally S, Khan A. Privacy aware IOTA ledger: Decentralized mixing and unlinkable IOTA transactions. Computer Networks. 2019;148: 361–372. doi: 10.1016/j.comnet.2018.11.019

54. Biryukov A, Tikhomirov S. Security and privacy of mobile wallet users in Bitcoin, Dash, Monero, and Zcash. Pervasive and Mobile Computing. 2019; 59: 101030. doi: 10.1016/j.pmcj.2019.101030

55. Castillo-Pérez S, Garcia-Alfaro J. Onion routing circuit construction via latency graphs. Computers & Security. 2013;37: 197–214. doi: 10.1016/j.cose.2013.03.003

56. Sakai K, Sun MT, Ku WS, Wu J. A framework for anonymous routing in delay tolerant networks. In: IEEE Transactions on Mobile Computing, Oct 10–13 2017; Toronto, Canada. IEEE, 2017 p. 1–10.

57. Motahari S Ziavras SG, Jones Q. Online anonymity protection in computer-mediated communication. IEEE Transactions on Information Forensics and Security. 2010;5(3): 570–580. doi: 10.1109/TIFS.2010.2051261

58. Singh L, Zhan J. Measuring topological anonymity in social networks. In: IEEE International Conference on Granular Computing, Nov 2–4 2007; Fremont, USA. IEEE, 2007. p. 770–774.

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