What is the dimension of citation space?

• Causal constraints in network structure require the development of novel methods.
• Tools from causal set theory can be applied to study citation networks.
• This can reveal differences in citation behaviour between subfields.
• We measure the dimension of the spacetime each citation network is closest to.
• Other directed acyclic graphs can be studied with these methods.

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.