In Japanese, a person who graduated the university called 社会人.

社会 is society and 人 is person. However society person does not seem natural English.

The word 社会人 was used in (1.2.1.2) How much time can you spend for learning? in Japanese version.

Replacement candidate:

person who graduate university

(feel incompatible) Even if a 30-years-old person did not graduate university, he may be 社会人.

if you have a full time job

(feel incompatible) Even if a 30-years-old person does not have a job, he may be 社会人.

Is it similar to the concept of "adult?"

I used same word in (5.3) Tuning for busy people, but in this case it just means busy people.

Related: the meaning of a word is its use in the language