WordNet records no synonym and no antonym for circulation. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the dissemination of copies of periodicals (as newspapers or magazines)
movement through a circuit; especially the movement of blood through the heart and blood vessels
(library science) the count of books that are loaned by a library over a specified period
number of copies of a newspaper or magazine that are sold
“by increasing its circulation the newspaper hoped to increase its advertising”
free movement or passage (as of cytoplasm within a cell or sap through a plant)
“ocean circulation is an important part of global climate”
the spread or transmission of something (as news or money) to a wider group or area
Synonyms, antonyms and the broader and narrower relations for circulation come from Princeton University’s WordNet. Full sources and licences.