MySQL 8.0

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CREATE TABLE Authors (
  `Author_ID` INTEGER,
  `Author_name` VARCHAR(4),
  `Paper_ID` INTEGER
);

INSERT INTO Authors
  (`Author_ID`, `Author_name`, `Paper_ID`)
VALUES
  ('1', 'Jack', '313'),
  ('2', 'Ray', '313'),
  ('2', 'Ray', '458'),
  ('3', 'Amy', '458'),
  ('1', 'Jack', '458'),
  ('2', 'Ray', '419'),
  ('3', 'Amy', '419'),
  ('2', 'Ray', '619'),
  ('3', 'Amy', '619');

Records: 9  Duplicates: 0  Warnings: 0


SELECT a1.Author_name AuthorA, 
       a2.Author_name AuthorB,
       COUNT(*) JointPapers
FROM Authors a1 INNER JOIN Authors a2
ON a1.Paper_ID = a2.Paper_ID AND a1.Author_ID < a2.Author_ID
GROUP BY a1.Author_name, a2.Author_name;


AuthorA
AuthorB
JointPapers


Jack
Ray
2

Jack
Amy
1

Ray
Amy
3


SELECT a1.Author_ID IDA, a1.Author_name AuthorA, 
       a2.Author_ID IDB, a2.Author_name AuthorB,
       COUNT(*) JointPapers
FROM Authors a1 INNER JOIN Authors a2
ON a1.Paper_ID = a2.Paper_ID AND a1.Author_ID < a2.Author_ID
GROUP BY a1.Author_ID, a1.Author_name, a2.Author_ID, a2.Author_name;


IDA
AuthorA
IDB
AuthorB
JointPapers


1
Jack
2
Ray
2

1
Jack
3
Amy
1

2
Ray
3
Amy
3