How to make an array as a tree that parent node and child node has a relationship?

Question

I have an array like this:

$visitors = [
    0 => ['id' => 1, 'visitor_id' => null],
    1 => ['id' => 2, 'visitor_id' => 1],
    2 => ['id' => 3, 'visitor_id' => 1],
    3 => ['id' => 4, 'visitor_id' => 2],
    4 => ['id' => 5, 'visitor_id' => 3],
    5 => ['id' => 6, 'visitor_id' => 3],
    6 => ['id' => 7, 'visitor_id' => 5],
    7 => ['id' => 8, 'visitor_id' => null],
    8 => ['id' => 9, 'visitor_id' => 8],
];

visitor_id is related with id, I want to build a tree like this

           1              8
          /\             /
         2  3           9
        /  / \
       4  5   6
         /
        7   

How can I get an array of the count of childs that every node have,for example

1 has 6 childs 2 has 1 childs 3 has 3 childs ...etc