Visibility graph analysis of Bitcoin price series

The Bitcoin market attracts special attentions for its inspirational advantages over the traditional currency system. It can be regarded also as a typical social experiment of rare item markets. Analyzing the records for Bitcoin price can deepen our understanding of this market and provide us a useful reference for rare item markets. In this paper, by means of the visibility graph algorithm we display multi-scale patterns of visible relationships in Bitcoin volatility series. It is found that the visibility graph of Bitcoin is scale-free and has a hierarchical structure. At different time scales, the system works subsequently with an identical dynamical mechanism. These behaviors are shared by other virtual currencies and even the gold price series. (C) 2019 Elsevier B.V. All rights reserved.