Standard introductory examples in Word2Vec, like
king - queen = man - woman and
tokyo - japan = london - uk, involve one-to-one relationships between words: Tokyo is the exclusive capital of Japan.
More generally, we might want to test for many-to-one relationships: e.g. we might want to ask if Kyoto is a city in Japan. I presume we are still interested in vectors of the form
tokyo - japan,
houston - us, etc., but these vectors are no longer equal.
Do these "relationship vectors" form a particularly interesting vector space? Do they sample some known distribution? How can I check a many-to-one relationship from the word embeddings?