Detecting core-periphery structures by surprise

Jeude, Jeroen van Lidth de; Caldarelli, Guido; Squartini, Tiziano

doi:10.1209/0295-5075/125/68001

Cited by 22 publications

(14 citation statements)

References 36 publications

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“…Hence, we also check for the presence of the "generalized" star graph structure also known as core-periphery structure, composed by a densely-connected core of nodes surrounded by a periphery of loosely-connected vertices. In order to do so, we implement a recently-proposed approach 20 , prescribing to minimize the score function known as bimodular surprise and reading…”

Section: /11mentioning

confidence: 99%

“…2 is the total number of node pairs, L = ∑ N i=1 ∑ N j=i+1 a i j is the total number of links, C is the number of node pairs in the core portion of the network, P is the number of node pairs in the periphery portion of the network, l c is the observed number of links in the core and l p is the observed number of links in the periphery. From a technical point of view, S is the p-value of a multivariate hypergeometric distribution 20 .…”

Section: /11mentioning

confidence: 99%

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

Lin,

Primicerio,

Squartini

et al. 2020

Preprint

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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 14 th January 2018 to 13 th July 2019, at the end of which the network has reached 8.216 users, 122.517 active channels and 2.732,5 transacted bitcoins. 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 binary and weighted versions 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.

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Section: /11mentioning

confidence: 99%

Section: /11mentioning

confidence: 99%

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

Lin,

Primicerio,

Squartini

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…allows 𝒲 ⫽ to be compactly rewritten in a way that nicely mirrors that of its binary counterpart [42,43].…”

Section: Core-periphery Detectionmentioning

confidence: 99%

The Weighted Bitcoin Lightning Network

Lin¹,

Marchese²,

Tessone³

et al. 2022

SSRN Journal

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“…allows W to be compactly rewritten in a way that nicely mirrors that of its binary counterpart 25,26 .…”

Section: Core-periphery Detectionmentioning

confidence: 99%

The Weighted Bitcoin Lightning Network

Lin¹,

Marchese²,

Tessone³

et al. 2021

Preprint

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The Bitcoin Lightning Network (BLN) was launched in 2018 to scale up the number of transactions between Bitcoin owners. Although several contributions concerning the analysis of the BLN binary structure have recently appeared in the literature, the properties of its weighted counterpart are still largely unknown. The present contribution aims at filling this gap, by considering the Bitcoin Lightning Network over a period of 18 months, ranging from 12 th January 2018 to 17 th July 2019, and focusing on its weighted, undirected, daily snapshot representation. As the study of the BLN weighted structural properties reveals, it is becoming increasingly 'centralised' at different levels, just as its binary counterpart: 1) the Nakamoto coefficient shows that the percentage of nodes whose degrees/strengths 'enclose' the 51% of the total number of links/total weight is rapidly decreasing; 2) the Gini coefficient confirms that several weighted centrality measures are becoming increasingly unevenly distributed; 3) the weighted BLN topology is becoming increasingly compatible with a core-periphery structure, with the largest nodes 'by strength' constituting the core of such a network, whose size keeps shrinking as the BLN evolves. Further inspection of the resilience of the weighted BLN shows that removing such hubs leads to the network fragmentation into many components, an evidence indicating potential security threats -as the ones represented by the so called 'split attacks'.

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Detecting core-periphery structures by surprise

Cited by 22 publications

References 36 publications

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

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

The Weighted Bitcoin Lightning Network

The Weighted Bitcoin Lightning Network

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