children.php

<?php

$list = [
    [1, 2],
    [2, 1],
    [3, 1],
    [4, 1],
    [5, 2],
    [6, 3],
    [7, 3],
    [8, 3],
    [9, 4],
    [10, 5],
    [11, 5],
    [12, 8],
    [13, 8],
    [14, 13],
    [15, 14],
    [16, 11],
    [17, 16],
    [18, 17],
];

$children = [];

foreach ($list as [$child, $parent]) {
    if (!isset($children[$child])) {
        $children[$child] = null;
    }

    $children[$parent][] = $child;
}

$children = merge($children);
print_r($children);

function merge($arr) {
    $xarr = $arr;

    foreach ($arr as $parent => $item) {
        if (!is_array($item)) continue;
        foreach ($item as $child) {
            if (isset($arr[$child])) {
                $arr[$parent] = array_unique(array_merge($arr[$parent], $arr[$child]));
            }
        }
    }

    if ($xarr != $arr) {
        return merge($arr);
    }

    return $xarr;
}