What is it called when authors trade citations?
In addition to the terms suggested by Scientist, another relatively common term is citation ring, here ring being used with the meaning (from Merriam-Webster):


  7 a : an exclusive combination of persons for a selfish and often corrupt purpose (as to control a market)
  b : GANG


Here are a few examples of usage of citation ring:


  SAGE Publications busts “peer review and citation ring,” 60 papers
  retracted


(Retraction Watch)


  Some other problems of the method were well outlined by Ulrich Korwitz (pp. 107-110): the problems of self-citation and the citation ring [...]


(T. Roper, "Citation Analysis of the Veterinary Literature: A Tool to Understanding Scientific Communication" in Libraries without Limits: Changing Needs — Changing Roles: Proceedings of the 6th European Conference of Medical and Health Libraries, Utrecht, 22–27 June 1998)