The functioning of the cryptocurrency Bitcoin relies on the open availability
of the entire history of its transactions. This makes it a particularly
interesting socio-economic system to analyse from the point of view of network
science. Here we analyse the evolution of the network of Bitcoin transactions
between users. We achieve this by using the complete transaction history from
December 5th 2011 to December 23rd 2013. This period includes three bubbles
experienced by the Bitcoin price. In particular, we focus on the global and
local structural properties of the user network and their variation in relation
to the different period of price surge and decline. By analysing the temporal
variation of the heterogeneity of the connectivity patterns we gain insights on
the different mechanisms that take place during bubbles, and find that hubs
(i.e., the most connected nodes) had a fundamental role in triggering the burst
of the second bubble. Finally, we examine the local topological structures of
interactions between users, we discover that the relative frequency of triadic
interactions experiences a strong change before, during and after a bubble, and
suggest that the importance of the hubs grows during the bubble. These results
provide further evidence that the behaviour of the hubs during bubbles
significantly increases the systemic risk of the Bitcoin network, and discuss
the implications on public policy interventions