n1 = 5;
    f[i_, j_] :=  With[{z := RandomInteger[j - 1]},If[i != j, RandomChoice[{z/n1, 1 - z/n1} -> {1, 0}], 0]];
    s = SparseArray[{{i_, j_} -> f[i, j]}, {n1, n1}];

n2 = 100;
s1 = Table[SparseArray[{{i_, j_} -> f[i, j]}, {n1, n1}], {k, n2}];