I have a tree (nested categories) stored as follows:

CREATE TABLE `category` (
  `category_id` int(10) unsigned NOT NULL AUTO_INCREMENT,
  `category_name` varchar(100) NOT NULL,
  `parent_id` int(10) unsigned DEFAULT NULL,
  PRIMARY KEY (`category_id`),
  UNIQUE KEY `category_name_UNIQUE` (`category_name`,`parent_id`),
  KEY `fk_category_category1` (`parent_id`,`category_id`),
  CONSTRAINT `fk_category_category1` FOREIGN KEY (`parent_id`) REFERENCES `category` (`category_id`) ON DELETE SET NULL ON UPDATE CASCADE
) ENGINE=InnoDB DEFAULT CHARSET=utf8 COLLATE=utf8_spanish_ci

I need to feed my client-side language (PHP) with node information (child+parent) so it can build the tree in memory. I can tweak my PHP code but I think the operation would be way simpler if I could just retrieve the rows in such an order that all parents come before their children. I could do that if I knew the level for each node:

SELECT category_id, category_name, parent_id
FROM category
ORDER BY level -- No `level` column so far :(

Can you think of a way (view, stored routine or whatever...) to calculate the node level? I guess it's okay if it's not real-time and I need to recalculate it on node modification.