Doctrine2 / SQL cooccurrences query - sql

Question

I actually want to write a Doctrine query (using the query builder), but first I want the SQL query. The query should retrieve the cooccurrences between the countries. In other words, I want to know how many times the country X collaborated with the country Y. FYI, a collaboration is when two (or more) inventors from different countries belong to the same patent.
This is my schema :
The Country class:
namespace Db\CreatorBundle\Entity;
use Doctrine\ORM\Mapping as ORM;
use Db\CreatorBundle\Entity\Inventor;
/**
* Country
*
* #ORM\Table()
* #ORM\Entity
*/
class Country
{
/**
* #var string
*
* #ORM\Column(name="name", type="string", length=255)
*/
private $name;
/**
* #var string
* #ORM\Id
* #ORM\Column(name="code", type="string", length=5)
*/
private $code;
/**
* #ORM\OneToMany(targetEntity="Inventor", mappedBy="country")
*/
private $inventors;
}
The Patent class:
namespace Db\CreatorBundle\Entity;
use Doctrine\ORM\Mapping as ORM;
use Db\CreatorBundle\Entity\Country;
/**
* Inventor
*
* #ORM\Table()
* #ORM\Entity
* #ORM\Entity(repositoryClass="Db\CreatorBundle\Entity\InventorRepository")
*/
class Inventor
{
/**
* #var string
* #ORM\Id
* #ORM\Column(name="fullName", type="string", length=255)
*/
private $fullName;
/**
* #ORM\ManyToMany(targetEntity="Patent", mappedBy="inventors")
*/
private $patents;
/**
* #ORM\ManyToOne(targetEntity="Country", inversedBy="inventors")
* #ORM\JoinColumn(name="country_code", referencedColumnName="code")
*/
private $country;
}
I have already written the query that retrieves the cooccurrences between the inventors, now I need the one for the countries.
So the result should be something like this :
Country | Country | Number of cooccurrences
US | FR | 30
US | KR | 12
US | JP | 91
CA | AU | 40
FR | AU | 23
FR | NL | 5
Oh, and thank you !
EDIT #1
This is my first query :
SELECT a.inventor_id, b.inventor_id, count(*) cnt
FROM inventors_patents a INNER JOIN inventors_patents b ON b.patent_id = a.patent_id
AND b.inventor_id > a.inventor_id
GROUP BY a.inventor_id, b.inventor_id
ORDER BY cnt DESC
The result looks like this :
AU1 AU2 8
AU1 AU3 7
AU1 AU4 7
AU2 AU3 6
AU2 AU5 4
AU3 AU6 3