= Coherent cyclic order of a digraph
= Coherent cyclic order
{synonym}
A cyclic ordering of a <directed graph> is considered unchanged by rotations or swaps of consecutive nonadjacent vertices. A representative is coherent when every backward edge $v_j\to v_i$ has a forward <directed path> from $v_i$ to $v_j$. Equivalently every edge is on a directed circuit that winds exactly once around the order. The number of backward edges on a circuit is invariant under the allowed changes. Every nontrivial <strongly connected directed graph> admits such an order.
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