从表A中选择所有ID，其中id不在数据透视表中

Question

I have a category table and a pivot table which determines the child categories. I wanted to use eloquent to select all the top level categories (categories that do not have a parent). I did want to do it with one eloquent query but haven't managed to get my head around it.

Database Structure

library_categories
    id
    title
    slug

library_category_relationships
    id
    parent_id
    category_id

Model

class LibraryCategory extends \Eloquent {

    public function children()
    {
        return $this->belongsToMany('LibraryCategory', 'library_category_relationships', 'parent_id', 'category_id');
    }

    public function parents()
    {
        return $this->belongsToMany('LibraryCategory', 'library_category_relationships', 'category_id', 'parent_id');
    }

}

Current Query (Located in a repository method)

$relationshipIds = DB::table('library_category_relationships')
                            ->select('category_id')
                            ->distinct()
                            ->get();

// Merge with id of 0 to avoid error in the next query if no relationships are found
$relationshipIds = array_merge([0], array_fetch($relationshipIds, 'category_id'));

return $this->model
            ->with($this->relationships)
            ->orderBy($orderBy, $sort)
            ->whereNotIn('id', $relationshipIds)
            ->paginate(Config::get('intranet.pagination.per_page'));

As you can see in the first half I fetch all the unique category ids from the pivot table that are children and in the second query I fetch the categories from that are not in the previous results.

Is it possible to some how include this in just one query? I would like to keep this contained within eloquent.

Thanks