I was on that site Sociopath Street. One of the posts was about love. They discussed the Greek versions of the word. It included a few types not commonly discussed. I thought it was interesting.
**The Greek forms of love fall into four or seven categories, depending on who is making the list; mania, ludus, and pragma are often left off the list, but I include them here as forms of love which might be more common for some sociopaths.
AGAPE - "selfless" or "godly" love, usually platonic or familial in nature, a love which prioritizes another person's well-being, even if it excludes oneself from being involved in the life of the other person
EROS - originally the love of beauty, usually expressed as romantic and/or sexual love for somebody who appeals to you on some aesthetic level (including possibly finding their mind attractive, not necessarily just their body)
LUDUS - "love of the game," a love which treats the other person as either a playmate or a plaything, potentially objectifying them for their ability to either share in games with you while manipulating people outside the relationship, also potentially objectifying them for how easy they are to manipulate and toy with; playing "hard-to-get" has been considered an expression of ludic love.
MANIA - "obsessive" love, often non-platonic in nature, a love which objectifies and over-idealizes another person, or places them as the whole center of one's attention, usually in a possessive or jealous manner
PHILIA - "love of the familiar" or "brotherly love," often directed toward siblings, teammates, and people who share your personal background; love of things and people which are comfortably known to you, even if the people in question are not necessarily like-minded
PRAGMA - "love of the practical," considered one of the sources of success for arranged marriages and relationships of convenience; love expressed through favours and beneficial tasks performed for another person; love which survives because it is mutually beneficial or convenient
STORGE - "love of the similar," often directed toward colleagues, friends within a topical community, and people who share some particular interest or activity or who are like-minded; love of people whose qualities you like out of their relatability to your own preferences