  Temporal graphs provide a useful model for many real-world networks.
Unfortunately the majority of algorithmic problems we might consider on such
graphs are intractable. There has been recent progress in defining structural
parameters which describe tractable cases by simultaneously restricting the
underlying structure and the times at which edges appear in the graph. These
all rely on the temporal graph being sparse in some sense. We introduce
temporal analogues of three increasingly restrictive static graph parameters --
cliquewidth, modular-width and neighbourhood diversity -- which take small
values for highly structured temporal graphs, even if a large number of edges
are active at each timestep. The computational problems solvable efficiently
when the temporal cliquewidth of the input graph is bounded form a subset of
those solvable efficiently when the temporal modular-width is bounded, which is
in turn a subset of problems efficiently solvable when the temporal
neighbourhood diversity is bounded. By considering specific temporal graph
problems, we demonstrate that (up to standard complexity theoretic assumptions)
these inclusions are strict.
