for my $s (0..$#a) { 
    @stack = ();
    @p = ();
    @delta = @sigma = @sigmainit;
    $sigma[$s] = 1;
    @d = @dinit;
    $d[$s] = 0;
    @queue = ();
    push(@queue,$s);
    while(@queue) {
        $v = shift(@queue);
        push(@stack,$v);
        for $w (0..$#a) {
            if ($a[$v][$w]) { 
                if ($d[$w] < 0) {
                    push(@queue,$w);
                    $d[$w] = $d[$v] + 1;
                }
                if ($d[$w] == $d[$v]+1) {
                    $sigma[$w] += $sigma[$v];
                    push(@{ $p[$w] },$v); 
                }
            }
        }
    }
    while (@stack) {
        $w = pop(@stack);
        foreach $v (@{ $p[$w] }) { 
            $delta[$v] += ($sigma[$v]/$sigma[$w]) * (1 + $delta[$w]);
        }
        if ($w != $s) {
            $b[$w] += $delta[$w];
        }
    }
}