The strong component structure of the barely subcritical directed configuration model

We study the behaviour of the largest components of the directed configuration model in the barely subcritical regime. We show that with high probability all strongly connected components in this regime are either cycles or isolated vertices and give an asymptotic distribution of the size of the $k$th largest cycle. This gives a configuration model analogue of a result of {\L}uczak and Seierstad for the binomial random digraph.