the three types of friendships as per a harvard university study

Utility friendships: Think about the relationships you have with people with whom you work, or with whom you do business. These relationships tend to be transactional in nature

Friendships based on pleasure: This type of relationship is based on mutual admiration because each person draws pleasure from the other. If a person finds their friend funny, interesting, and a source of enjoyment, it is likely a friendship of pleasure

Perfect friendships: Perfect friendships are those between people who have a mutual love for something that not only brings them together, but elevates their behavior to virtue. A relationship is perfect not when it is based on utility or pleasure, but when it is focused on improving the circumstance of the other person