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

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.

[1]  Mahdi Jalili,et al.  Enhancing Synchronizability of Diffusively Coupled Dynamical Networks: A Survey , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Cassandra E. Dodge,et al.  Use of Bitcoin in Darknet Markets: Examining Facilitative Factors on Bitcoin-Related Crimes , 2018 .

[3]  Geoffrey Lightfoot,et al.  Price Fluctuations and the Use of Bitcoin: An Empirical Inquiry , 2015, Int. J. Electron. Commer..

[4]  Bo Hu,et al.  General dynamics of topology and traffic on weighted technological networks. , 2005, Physical review letters.

[5]  Alex Biryukov,et al.  Security and privacy of mobile wallet users in Bitcoin, Dash, Monero, and Zcash , 2019, Pervasive Mob. Comput..

[6]  Shauhrat S Chopra,et al.  A network-based framework for assessing infrastructure resilience: a case study of the London metro system , 2016, Journal of The Royal Society Interface.

[7]  Andrej Mosebach Synchronization of oscillators in complex networks , 2015 .

[8]  Tatsuya Akutsu,et al.  Protein domain networks: Scale-free mixing of positive and negative exponents , 2006 .

[9]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[10]  Radu Marculescu,et al.  Weighted Betweenness Preferential Attachment: A New Mechanism Explaining Social Network Formation and Evolution , 2018, Scientific Reports.

[11]  Bart Preneel,et al.  Towards Measuring Anonymity , 2002, Privacy Enhancing Technologies.

[12]  S. Boccaletti,et al.  Synchronizing weighted complex networks. , 2006, Chaos.

[13]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[14]  Michele Bellingeri,et al.  Robustness of weighted networks , 2018 .

[15]  Ganesh Bagler,et al.  Analysis of the airport network of India as a complex weighted network , 2004, cond-mat/0409773.

[16]  Lisa Singh,et al.  Measuring Topological Anonymity in Social Networks , 2007, 2007 IEEE International Conference on Granular Computing (GRC 2007).

[17]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[18]  Jie Wu,et al.  A framework for anonymous routing in delay tolerant networks , 2017, 2017 IEEE 25th International Conference on Network Protocols (ICNP).

[19]  C. Leung,et al.  Weighted assortative and disassortative networks model , 2006, physics/0607134.

[20]  David K Campbell,et al.  Editorial: The pre-history of Chaos-An Interdisciplinary Journal of Nonlinear Science. , 2015, Chaos.

[21]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[22]  S. Low,et al.  The "robust yet fragile" nature of the Internet. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Soummya Kar,et al.  Topology for Distributed Inference on Graphs , 2006, IEEE Transactions on Signal Processing.

[24]  Takamitsu Watanabe,et al.  Enhancing the spectral gap of networks by node removal. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Marko Vukolic,et al.  The Quest for Scalable Blockchain Fabric: Proof-of-Work vs. BFT Replication , 2015, iNetSeC.

[26]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[27]  Woo-Sung Jung,et al.  Characteristics of the Korean stock market correlations , 2006 .

[28]  Joaquín García,et al.  Onion routing circuit construction via latency graphs , 2013, Comput. Secur..

[29]  Alessandro Vespignani,et al.  Modeling the evolution of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Sherali Zeadally,et al.  Privacy aware IOTA ledger: Decentralized mixing and unlinkable IOTA transactions , 2019, Comput. Networks.

[31]  Michael Chertkov,et al.  Synchronization in complex oscillator networks and smart grids , 2012, Proceedings of the National Academy of Sciences.

[32]  Albert-László Barabási,et al.  Scale-Free Networks: A Decade and Beyond , 2009, Science.

[33]  Boleslaw K. Szymanski,et al.  Optimizing Synchronization, Flow, and Robustness in Weighted Complex Networks , 2012 .

[34]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[35]  István Csabai,et al.  Do the Rich Get Richer? An Empirical Analysis of the Bitcoin Transaction Network , 2013, PloS one.

[36]  A. Hagberg,et al.  Rewiring networks for synchronization. , 2008, Chaos.

[37]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[38]  X. Cai,et al.  Empirical analysis of a scale-free railway network in China , 2007 .

[39]  V. Latora,et al.  Efficiency of scale-free networks: error and attack tolerance , 2002, cond-mat/0205601.

[40]  Quentin Jones,et al.  Online Anonymity Protection in Computer-Mediated Communication , 2010, IEEE Transactions on Information Forensics and Security.

[41]  E. Yasunori,et al.  Agglomerative Hierarchical Clustering for Data with Tolerance , 2007, 2007 IEEE International Conference on Granular Computing (GRC 2007).

[42]  F. Atay,et al.  Network synchronization: Spectral versus statistical properties , 2006, 0706.3069.

[43]  Michael K. Reiter,et al.  Crowds: anonymity for Web transactions , 1998, TSEC.

[44]  Juan Carlos De Martin,et al.  The CLoTH Simulator for HTLC Payment Networks with Introductory Lightning Network Performance Results , 2018, Inf..

[45]  Massimo Marchiori,et al.  Economic small-world behavior in weighted networks , 2003 .

[46]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[47]  Jurgen Kurths,et al.  Rewiring hierarchical scale-free networks: Influence on synchronizability and topology , 2017, 1707.04057.

[48]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[49]  Andrea Flori CRYPTOCURRENCIES IN FINANCE: REVIEW AND APPLICATIONS , 2019, International Journal of Theoretical and Applied Finance.

[50]  Christian Decker,et al.  A Fast and Scalable Payment Network with Bitcoin Duplex Micropayment Channels , 2015, SSS.

[51]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[52]  Richard M. Murray,et al.  Stability analysis of stochastically varying formations of dynamic agents , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[53]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[54]  Daniel Dajun Zeng,et al.  Evolutionary dynamics of cryptocurrency transaction networks: An empirical study , 2018, PloS one.

[55]  Cryptocurrencies as a Financial Asset: A Systematic Analysis , 2019 .