Matrix Algorithms

Transitive Closure

Determine reachability between all pairs of vertices in a directed graph. Using a variation of the Floyd-Warshall algorithm, we iteratively discover transitive paths i → k → j in O(V³).

Time ComplexityO(V³)

Space ComplexityO(V²)

Start Interactive Simulator

Reachability Matrix

The output is a boolean matrix where M[i][j] = 1 indicates that a path exists from i to j, no matter how many edges it takes.

Path Materialization

This algorithm "materializes" abstract connectivity into direct matrix entries, which is crucial for static analysis and logic inference.

🖱️ Click Matrix cells to toggle connections • ↔️ Drag nodes to move

Direct Edge

Transitive Path

Loading Lab...

Matrix Algorithms

Transitive Closure

Determine reachability between all pairs of vertices in a directed graph. Using a variation of the Floyd-Warshall algorithm, we iteratively discover transitive paths i → k → j in O(V³).

Time ComplexityO(V³)

Space ComplexityO(V²)

Start Interactive Simulator

Reachability Matrix

The output is a boolean matrix where M[i][j] = 1 indicates that a path exists from i to j, no matter how many edges it takes.

Path Materialization

This algorithm "materializes" abstract connectivity into direct matrix entries, which is crucial for static analysis and logic inference.

🖱️ Click Matrix cells to toggle connections • ↔️ Drag nodes to move

Direct Edge

Transitive Path