比特币网络的传染
Contagion in Bitcoin networks
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比特币交易的Google矩阵。在过去的几个季度中，网络规模包含约600万用户（节点），约有1.5亿笔交易。从PageRank和CheiRank概率，类似于贸易进口和出口，我们确定每个用户的无量纲贸易差额和模型的网络上的传染传播，假设一个用户破产，如果其余额超过一定的无量纲阈值$κ$。我们发现$κ<κ_c\approx0.1$在几乎所有用户都破产的情况下发生了相变。对于$κ>0.55$，几乎所有用户都是安全的。我们发现，即使距离临界阈值$κ_c$的顶级PageRank和CheiRank用户，作为一个纸牌屋，迅速下降到破产。我们将这种影响归因于这些顶级用户之间的强大互连，我们使用简化的Google矩阵算法确定。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，这项研究模型的传染在真正的金融网络。
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 $κ$. We find that the phase transition takes place for $κ<κ_c\approx0.1$ with almost all users going bankrupt. For $κ>0.55$ almost all users remain safe. We find that even on a distance from the critical threshold $κ_c$ 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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