The crux of the algorithm comes in determining whether a node is the root of a strongly connected component. DoTo thisdo this, each node is given a depth search index <tt>v.index</tt>, which numbers the nodes consecutively in the order in which they are discovered. In addition, each node is assigned a value <tt>v.lowlink</tt> that satisfies <tt>v.lowlink := min {v'.dfs: v' is reachable from v}</tt>. Therefore <tt>v</tt> is the root of a strongly connected component if and only if <tt>v.lowlink = v.index</tt>. The value <tt>v.lowlink</tt> is computed during the depth first search such that it is always known when needed.
