  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.
