Floyd's algorithm finds the cost of the least cost path (or the path itself) between every pair of vertices.
Often we only want to know if there is a path between any two vertices (and ignore costs).
Warshall's algorithm is a specialized (but earlier) version of Floyd's algorithm that solves this problem, called the transitive closure of a graph.
Given a directed graph G = (V,E), represented by an adjacency matrix A[i,j], where A[i,j] = 1 if (i,j) is in E, compute the matrix P, where P[i,j] is 1 if there is a path of length greater than or equal to 1 from i to j.
Warshall (int N, bmatrix &A, bmatrix &P)
{
int i,j,k;
for (i = 0; i < N; i++)
for (j = 0; j < N; j++)
/* There's a path if there's an edge */
P[i][j] = A[i][j];
for (k = 0; k < N; k++)
for (i = 0; i < N; i++)
for (j = 0; j < N; j++)
if (! P[i][j])
P[i][j] = P[i][k] && P[k][j];
} /* Warshall */
Clearly the algorithm is O(N^3).