  In many complex networks the vertices are ordered in time, and edges
represent causal connections. We propose methods of analysing such directed
acyclic graphs taking into account the constraints of causality and
highlighting the causal structure. We illustrate our approach using citation
networks formed from academic papers, patents, and US Supreme Court verdicts.
We show how transitive reduction reveals fundamental differences in the
citation practices of different areas, how it highlights particularly
interesting work, and how it can correct for the effect that the age of a
document has on its citation count. Finally, we transitively reduce null models
of citation networks with similar degree distributions and show the difference
in degree distributions after transitive reduction to illustrate the lack of
causal structure in such models.
