ItThe ismain obviouslycrux crucial forof the algorithm that when returning from a subtree it is determined for each nodedetermining whether thata node is in the root of a strongly connected component. For that purpose, each node is given a depth search index v.dfs, which numbers the nodes consecutively in the order in which they are "discovered" by the depth first search. In addition, a value v.lowlink is assigned, such that v.lowlink := min {v'.dfs: v' is reachable from v}. Therefore: v is the root of a strongly connected component if and only if v.lowlink = v.dfs. v.lowlink can be computed during the depth first search in such a way that the value is known at the time of the query.
