(* Computation of Transitive Closure by Warshall Algorithm *)



tClosure[m_] := Sign[MatrixPower[m, Length[m]]]



Warshall[mat_] := Module[{i, j, k, n, m},

    m = mat; n = Length[m];

    For[k = 1, k <= n, k++,

      For[i = 1, i <= n, i++,

        For[j = 1, j <= n, j++, If[m[[i, k]] == 1 && m[[k, j]] == 1,

            m[[i, j]] = 1]]]]; m]



m = Table[Random[Integer, {0, 1}], {i, 1, 10}, {j, 1, 10}]



Timing[Warshall[m]][[1]]

Timing[tClosure[m]][[1]]