In this paper, we have shown that a graph is a circular arc graph if and only if the corresponding symmetric digraph with loops is a circular arc digraph. We characterize circular arc digraphs and circular arc graphs using circular ordering of their edges. We also characterize a circular arc graph as a union of an interval graph and a threshold graph. Finally, we characterize proper interval bigraphs and proper circular arc bigraphs using two linear orderings of their vertex set. © 2016 Elsevier B.V.