  Citation networks represent the flow of information between agents. They are
constrained in time and so form directed acyclic graphs which have a causal
structure. Here we provide novel quantitative methods to characterise that
structure by adapting methods used in the causal set approach to quantum
gravity by considering the networks to be embedded in a Minkowski spacetime and
measuring its dimension using Myrheim-Meyer and Midpoint-scaling estimates. We
illustrate these methods on citation networks from the arXiv, supreme court
judgements from the USA, and patents and find that otherwise similar citation
networks have measurably different dimensions. We suggest that these
differences can be interpreted in terms of the level of diversity or narrowness
in citation behaviour.
