英文标题：
《Contagion in Bitcoin networks》
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作者：
C\\\'elestin Coquid\\\'e, Jos\\\'e Lages, and Dima L. Shepelyansky
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最新提交年份：
2019
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英文摘要：
  We construct the Google matrices of bitcoin transactions for all year quarters during the period of January 11, 2009 till April 10, 2013. During the last quarters the network size contains about 6 million users (nodes) with about 150 million transactions. From PageRank and CheiRank probabilities, analogous to trade import and export, we determine the dimensionless trade balance of each user and model the contagion propagation on the network assuming that a user goes bankrupt if its balance exceeds a certain dimensionless threshold $\\kappa$. We find that the phase transition takes place for $\\kappa<\\kappa_c\\approx0.1$ with almost all users going bankrupt. For $\\kappa>0.55$ almost all users remain safe. We find that even on a distance from the critical threshold $\\kappa_c$ the top PageRank and CheiRank users, as a house of cards, rapidly drop to the bankruptcy. We attribute this effect to strong interconnections between these top users which we determine with the reduced Google matrix algorithm. This algorithm allows to establish efficiently the direct and indirect interactions between top PageRank users. We argue that this study models the contagion on real financial networks.
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中文摘要：
我们构建了2009年1月11日至2013年4月10日期间所有年度季度的谷歌比特币交易矩阵。在过去几个季度，网络规模约为600万用户（节点），交易量约为1.5亿。根据PageRank和CheiRank概率，类似于贸易进出口，我们确定每个用户的无量纲贸易余额，并假设用户的余额超过某个无量纲阈值$\\ kappa$，则建立网络上的传染传播模型。我们发现，在几乎所有用户破产的情况下，相变发生在$\\ kappa<\\ kappa\\u c\\approx0.1$。对于$\\ kappa>0.55$，几乎所有用户都保持安全。我们发现，即使距离临界值$\\ kappa\\c$很远，顶级PageRank和CheiRank用户作为一个纸牌之家，也会迅速走向破产。我们将这种影响归因于这些顶级用户之间的强大互联，这是我们通过简化的谷歌矩阵算法确定的。该算法可以有效地建立顶级PageRank用户之间的直接和间接交互。我们认为，这项研究模拟了真实金融网络上的传染。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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