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MySQL one to many relationship, with shared values

I have a MySQL DB with 3 tables.

profile, p_tags, tags

DB:

profile
pid | name

ptags
ptid | pid | tagid

tags
tagid | tag

The DB looks something like this

profile
pid | name
 1    Randy
 2    Jeff
 3    Mike

ptags
ptid | pid | tagid
 1      1      1
 2      1      2 
 3      2      1
 4      2      3 
 5      3      1
 6      3      2
 7      3      3 

tags
tagid | tag
  1     science
  2     filosophy
  3     hydrology

What I need is to create a query that displays The names in the profile that have shared tags and the total shared tags

IE

Results
Name  | Name2 | Count
Randy - Jeff - 1
Randy - Mike - 2
Jeff - Randy - 1
Jeff - Mike - 2 
Mike - Randy - 2
Mike - Jeff - 2

And so on.

I dunno if I explained it correctly.

I read

https://www.simple-talk.com/sql/t-sql-programming/divided-we-stand-the-sql-of-relational-division/

From a link from another post similar to this one, but just can't get my head around it :).

SQLFiddle: http://sqlfiddle.com/#!9/42bde6

in query use join:

SELECT p1.name Name1, p2.name Name2, Count(tagid)
FROM ptags AS t1
INNER JOIN ptags AS t2 ON t2.tagid = t1.tagid and t2.ptid <> t1.ptid 
INNER JOIN profile AS p1 ON p1.pid = t1.pid 
INNER JOIN profile AS p2 ON p2.pid = t2.pid 
GROUP BY p1.name, p2.name

and if you need only one row for pair of firstname then try this:

SELECT p1.firstname Name1, p2.firstname Name2, Count(t1.tagid)
FROM profile_hashtags AS t1
INNER JOIN profile_hashtags AS t2 
  ON t2.tagid = t1.tagid and t2.pHid > t1.pHid 
INNER JOIN `profile` AS p1 ON p1.pid = t1.pid 
INNER JOIN `profile` AS p2 ON p2.pid = t2.pid 
GROUP BY p1.firstname, p2.firstname;

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