<P> A directed graph is strongly connected if and only if it has an ear decomposition, a partition of the edges into a sequence of directed paths and cycles such that the first subgraph in the sequence is a cycle, and each subsequent subgraph is either a cycle sharing one vertex with previous subgraphs, or a path sharing its two endpoints with previous subgraphs . </P> <P> According to Robbins' theorem, an undirected graph may be oriented in such a way that it becomes strongly connected, if and only if it is 2 - edge - connected . One way to prove this result is to find an ear decomposition of the underlying undirected graph and then orient each ear consistently . </P>

Decomposing a digraph into a dag of scc