Lightning Network: a second path towards centralisation of the Bitcoin economy

The Bitcoin Lightning Network (BLN), a so-called "second layer" payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the three representations above, we find that the total volume of transacted bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin Lightning Network) is, in fact, ~0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the Undirected Binary Configuration Model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks.

[1]  Mark E. J. Newman The structure and dynamics of networks , 2006, Princeton studies in complexity.

[2]  V. Latora,et al.  Centrality measures in spatial networks of urban streets. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Jerry L. Harbour A Family of Measures , 2017 .

[4]  Bitcoin Proof of Stake: A Peer-to-Peer Electronic Cash System , 2020 .

[5]  Ingo Scholtes,et al.  Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks , 2013, Physical review letters.

[6]  Phillip Bonacich Some unique properties of eigenvector centrality , 2007, Soc. Networks.

[7]  László Gulyás,et al.  Topological Analysis of Bitcoin's Lightning Network , 2019, MARBLE.

[8]  Qiang Guo,et al.  Locating influential nodes via dynamics-sensitive centrality , 2016, Scientific reports.

[9]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[10]  Florian Tschorsch,et al.  Discharged Payment Channels: Quantifying the Lightning Network's Resilience to Topology-Based Attacks , 2019, 2019 IEEE European Symposium on Security and Privacy Workshops (EuroS&PW).

[11]  Diego Garlaschelli,et al.  Analytical maximum-likelihood method to detect patterns in real networks , 2011 .

[12]  P. Bonacich Power and Centrality: A Family of Measures , 1987, American Journal of Sociology.

[13]  Francisco Aparecido Rodrigues Network Centrality: An Introduction , 2019 .

[14]  Stephen P. Borgatti Centrality and network flow , 2005, Soc. Networks.

[15]  Silvia Bartolucci,et al.  A Percolation Model for the Emergence of the Bitcoin Lightning Network , 2019, ArXiv.

[16]  Mark E. J. Newman A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[17]  M. Newman,et al.  Statistical mechanics of networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Yves Zenou,et al.  From Assortative to Dissortative Networks: The Role of Capacity Constraints , 2010, Adv. Complex Syst..

[19]  Guido Caldarelli,et al.  Detecting Core-Periphery Structures by Surprise , 2018, ArXiv.

[20]  Khadija Iqbal An introduction , 1996, Neurobiology of Aging.

[21]  Satoshi Nakamoto Bitcoin : A Peer-to-Peer Electronic Cash System , 2009 .

[22]  James N. Morgan The Anatomy of Income Distribution , 1962 .

[23]  Yves Zenou,et al.  Nestedness in Networks: A Theoretical Model and Someapplications , 2012 .

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