metropolitan core vs principal city

metropolitan core

noun
  • Synonym of central city (“the main city of a metropolitan area; particularly one containing multiple cities”). 

  • Used other than figuratively or idiomatically: see metropolitan, core. 

principal city

noun
  • Synonym of central city (“the main city of a metropolitan area; particularly one containing multiple cities”). 

  • Used other than figuratively or idiomatically: see principal, city. 

How often have the words metropolitan core and principal city occurred in a corpus of books? (source: Google Ngram Viewer )