A related but weaker concept is that of a strongly connected component.

Check whether any strongly connected component contains both a variable and its negation.

Otherwise, if w has not yet been assigned to a strongly connected component:

Therefore is the root of a strongly connected component if and only if .

Consider the automaton as a directed graph and decompose it into strongly connected components.

Thus, even for tournaments that are not transitive, the strongly connected components of the tournament may be totally ordered.

Stack P contains vertices that have not yet been determined to belong to different strongly connected components from each other.

Check whether there is a non-trivial strongly connected component that is both reachable and contains a final state.

Visually, they form alternative routes from "In" to "Out", like tubes bending around the central strongly connected component.

Finding strongly connected components.

Kosaraju's algorithm, an algorithm to find the strongly connected component of a directed graph.

The crux of the algorithm comes in determining whether a node is the root of a strongly connected component.

The algorithm pops the stack up to and including the current node, and presents all of these nodes as a strongly connected component.

For, if it is not acyclic, each of its strongly connected components must either be entirely contained in or entirely disjoint from any closed set.

The strongly connected components of a directed graph G are its maximal strongly connected subgraphs.

Construct the implication graph of the instance, and find its strongly connected components using any of the known linear-time algorithms for strong connectivity analysis.

The algorithm takes a directed graph as input, and produces a partition of the graph's vertices into the graph's strongly connected components.

Strongly Connected Component: A collection of nodes in which there exists a directed path from any node to any other.

Using the graph, the optimizer can then cluster the strongly connected components (SCC) and separate vectorizable statements from the rest.

The root node is simply the first node of the strongly connected component which is encountered during the depth-first traversal.

The concept of the "root" applies only to this algorithm (outside of the algorithm, a strongly connected component has no single "root" node).

Some of his well-known algorithms include Tarjan's off-line least common ancestors algorithm, and Tarjan's strongly connected components algorithm.

Java implementation for computation of strongly connected components in the jBPT library (see StronglyConnectedComponents class).

An example of this is Kosaraju's algorithm for strongly connected components, which applies depth first search twice, once to the given graph and a second time to its reversal.

The function performs a single depth-first search of the graph, finding all successors from the node , and reporting all strongly connected components of that subgraph.