I have a table that looks like:

    CREATE TABLE `connections` (
    `connection_id` bigint(20) unsigned NOT NULL AUTO_INCREMENT,
    `service_id` smallint(5) unsigned DEFAULT NULL,
    `parent_id` bigint(20) unsigned DEFAULT NULL,
    `child_id` bigint(20) unsigned DEFAULT NULL,
    PRIMARY KEY (`connection_id`),
    UNIQUE KEY `primary_child` (`parent_id`,`child_id`),
    UNIQUE KEY `child_primary` (`child_id`,`parent_id`)
    ) ENGINE=InnoDB  DEFAULT CHARSET=utf8;

I need to do lookups on child_id and get information about parent_id and vice versa.

Ie:

    SELECT COUNT(`parent_id`) FROM `connections` WHERE `child_id` = 'x'

or

    SELECT COUNT(`child_id`) FORM `connections` WHERE `parent_id` = 'x'

And some more advanced queries like:

    SELECT DISTINCT `parent_id`
    FROM `connections` `c1`
    INNER JOIN `connections` `c2`
    ON `c1`.`parent_id` = `c2`.`parent_id`
    WHERE `c1`.`child_id` = 'x'
    AND `c2`.`child_id` = 'y'

I'm looking to get a better idea of the most efficient index structure to get quick responses from all the above query examples.

It should be noted that the child/parent pairs will be unique.

Thanks,