imap_thread() returns threads, but are confined to the current open mailbox you defined in imap_open(). This is not useful for, lets say, getting full threads ( from "Sent Messages" and "Inbox" [took me a day to figure this out]). 

If you compare threads on Outlook vs gmail.com you will find that Outlook determines threads by subject title, not actual parent > child relationships. 

Gmail however, seems to get threads right, but does not include mail you send using their web interface in  {imap.google.com:993/imap/ssl}Sent Messages . What this means is that threads using php imap won't be perfect for gmail.

If you send mail using Outlook (or any mail client), gmail.com does put it in their "Sent Mail".

So all in all, threads for PHP imap are not perfect. But I blame the imap specifications (DEAR IMAP GUYS, please add better uids and parent ids. thx Chris) more than PHP

So I created the Outlook method for threading (comparing subjects) below:

<?php 
$imap         = imap_open('{imap.gmail.com:993/imap/ssl}INBOX', '[email protected]', 'yourpassword');
$subject     = 'Item b';
$threads     = array();

//remove re: and fwd:
$subject = trim(preg_replace("/Re\:|re\:|RE\:|Fwd\:|fwd\:|FWD\:/i", '', $subject));

//search for subject in current mailbox
$results = imap_search($imap, 'SUBJECT "'.$subject.'"', SE_UID);

//because results can be false
if(is_array($results)) {
    //now get all the emails details that were found 
    $emails = imap_fetch_overview($imap, implode(',', $results), FT_UID);
    
    //foreach email 
    foreach ($emails as $email) {
        //add to threads
        //we date date as the key because later we will sort it
        $threads[strtotime($email->date)] = $email;
    }    
}

//now reopen sent messages
imap_reopen($imap, '{imap.gmail.com:993/imap/ssl}Sent Messages');

//and do the same thing

//search for subject in current mailbox
$results = imap_search($imap, 'SUBJECT "'.$subject.'"', SE_UID);

//because results can be false
if(is_array($results)) {
    //now get all the emails details that were found 
    $emails = imap_fetch_overview($imap, implode(',', $results), FT_UID);
    
    //foreach email 
    foreach ($emails as $email) {
        //add to threads
        //we date date as the key because later we will sort it
        $threads[strtotime($email->date)] = $email;
    }    
}

//sort keys so we get threads in chronological order 
ksort($threads);

echo '<pre>'.print_r($threads, true).'</pre>';
exit;
?>

so if you are going to use imap_thread() for something useful. This is probably the most optimal way I can think of:

<?php 
$imap = imap_open('{imap.gmail.com:993/imap/ssl}INBOX', '[email protected]', 'password');
$threads = $rootValues = array();

$thread = imap_thread($imap);
$root = 0;

//first we find the root (or parent) value for each email in the thread
//we ignore emails that have no root value except those that are infact
//the root of a thread

//we want to gather the message IDs in a way where we can get the details of
//all emails on one call rather than individual calls ( for performance )

//foreach thread
foreach ($thread as $i => $messageId) {
    //get sequence and type
    list($sequence, $type) = explode('.', $i);
    
    //if type is not num or messageId is 0 or (start of a new thread and no next) or is already set 
    if($type != 'num' || $messageId == 0 
       || ($root == 0 && $thread[$sequence.'.next'] == 0)
       || isset($rootValues[$messageId])) {
        //ignore it
        continue;
    }
    
    //if this is the start of a new thread
    if($root == 0) {
        //set root
        $root = $messageId;
    }
    
    //at this point this will be part of a thread
    //let's remember the root for this email
    $rootValues[$messageId] = $root;
    
    //if there is no next
    if($thread[$sequence.'.next'] == 0) {
        //reset root
        $root = 0;
    }
}

//now get all the emails details in rootValues in one call
//because one call for 1000 rows to a server is better 
//than calling the server 1000 times  
$emails = imap_fetch_overview($imap, implode(',', array_keys($rootValues)));

//foreach email 
foreach ($emails as $email) {
    //get root
    $root = $rootValues[$email->msgno];
    
    //add to threads
    $threads[$root][] = $email;
}    

//there is no need to sort, the threads will automagically in chronological order
echo '<pre>'.print_r($threads, true).'</pre>';
imap_close($imap);
exit;
?>

I figure other people may benefit from an explanation of the resulting array, My understanding is:

Key: Essentially a node ID
Num: The mail ID (where 0 indicates the start of a conversation)
Next: The node ID of the first child (where 0 indicates there are no children)
Branch: The node ID of the next sibling (where 0 indicates there is no sibling)