a digraph is a SCC iff it has an ear decomposition
proof: forward direction (ear decomposition scc) is trivial to show scc ear decomposition, we can start with any cycle (this can be a single node) WLOG, assume this cycle is just node . then, at each step: let be a node not currently in our component. Let the path be the next ear.
after all nodes are added, join all remaining single edges