  Directed networks are broadly used to represent asymmetric relationships
among units. Co-clustering aims to cluster the senders and receivers of
directed networks simultaneously. In particular, the well-known spectral
clustering algorithm could be modified as the spectral co-clustering to
co-cluster directed networks. However, large-scale networks pose great
computational challenges to it. In this paper, we leverage sketching techniques
and derive two randomized spectral co-clustering algorithms, one
\emph{random-projection-based} and the other \emph{random-sampling-based}, to
accelerate the co-clustering of large-scale directed networks. We theoretically
analyze the resulting algorithms under two generative models -- the stochastic
co-block model and the degree-corrected stochastic co-block model, and
establish their approximation error rates and misclustering error rates,
indicating better bounds than the state-of-the-art results of co-clustering
literature. Numerically, we design and conduct simulations to support our
theoretical results and test the efficiency of the algorithms on real networks
with up to millions of nodes. A publicly available R package \textsf{RandClust}
is developed for better usability and reproducibility of the proposed methods.
