What Wide is to width as gay is to?

The relationship between "wide" and "width" is that "wide" is the adjective form describing the extent of something horizontally, while "width" is the noun form referring to the measurement of that extent. Similarly, the relationship between "gay" and its counterpart could be seen as "gay" being the adjective form describing someone's sexual orientation or identity, while the counterpart could be "homosexuality," which is the noun form referring to that sexual orientation or identity.