  Methodologies to infer financial networks from the price series of
speculative assets vary, however, they generally involve bivariate or
multivariate predictive modelling to reveal causal and correlational structures
within the time series data. The required model complexity intimately relates
to the underlying market efficiency, where one expects a highly developed and
efficient market to display very few simple relationships in price data. This
has spurred research into the applications of complex nonlinear models for
developed markets. However, it remains unclear if simple models can provide
meaningful and insightful descriptions of the dependency and interconnectedness
of the rapidly developed cryptocurrency market. Here we show that multivariate
linear models can create informative cryptocurrency networks that reflect
economic intuition, and demonstrate the importance of high-influence nodes. The
resulting network confirms that node degree, a measure of influence, is
significantly correlated to the market capitalisation of each coin
($\rho=0.193$). However, there remains a proportion of nodes whose influence
extends beyond what their market capitalisation would imply. We demonstrate
that simple linear model structure reveals an inherent complexity associated
with the interconnected nature of the data, supporting the use of multivariate
modelling to prevent surrogate effects and achieve accurate causal
representation. In a reductive experiment we show that most of the network
structure is contained within a small portion of the network, consistent with
the Pareto principle, whereby a fraction of the inputs generates a large
proportion of the effects. Our results demonstrate that simple multivariate
models provide nontrivial information about cryptocurrency market dynamics, and
that these dynamics largely depend upon a few key high-influence coins.
