▼ Although βασιλεύς (basileus) lacks the article it is definite due to contextual and syntactical considerations. See ExSyn 263.

▼ Nathanael’s confession - You are the Son of God; you are the King of Israel - is best understood as a confession of Jesus’ messiahship. It has strong allusions to Ps 2:6–7, a well-known messianic psalm. What Nathanael’s exact understanding was at this point is hard to determine, but “son of God” was a designation for the Davidic king in the OT, and Nathanael parallels it with King of Israel here.