What is love? Not to recall certain catchy songs popular on the internet in the 2000s, I wanted to try to give a definition. The problem of getting definitions for commonly used words is a well known problem in philosophy, so as usual I will instead that I am giving my definition and hope that it hits an adequate amount of the way that people use the word.
The definition that I am using is "A fulfilling connection to something or someone you can treat as an entity with volition towards you."
I'm somewhat uncertain about this definition. I think it covers everything I care about, though I neglect smaller entities below for now (such as, e.g., pets or various digital entities). When I say volition I mean that you ascribe some sort of agentic behavior to it that you get a fulfilling connection from, not that it necessarily loves you back in the same way.
There is also an idea of a passive sense vs an active sense of fulfilling connection. To differentiate this I call one 'appreciation' or 'attraction', and the other 'love'. You may appreciate someone but until they act with volition towards you in a relevant manner, can you say that you truly love them as a friend?
The first category of loves that I identify are the loves of others—family, friends, and erotics/paramours.
Family
In the vast majority of cases, you are born into the family that you will spend your life with. In the norm, there are two parents, some number of siblings, and some amount of more distant cousins. At the extremes there may be more parents (via divorces), many siblings, hundreds of cousins—or perhaps an orphan with no relatives, or only one relative. But the core idea here is around the three generation nuclear family.
Part of the atomicity of trying to break down love is that it becomes hard to say 'familial love is made out of some other thing'. Familial love is...familial love. Perhaps it is a recognition of the self, perhaps it is biological game theory. But we have a tendency to love those in our families by default, unless they do something to violate that love.
In line with various writings on social roles, we put different levels of expectations on those we love. If we consider a parent, a sibling, and a child to all be roughly the same distance from us conceptually (which they also are biologically), that doesn't mean that we have the same expectations for them.
In line with the fact that we recognize the similarity between those we love in our family and ourselves, we hold them to similar standards. From our progenitors, we have the highest standards, from our siblings we have standards perhaps similar to those we set for ourselves, and from our children the bar is the lowest.
We can confirm this by looking at tendencies (unfortunately, lacking numbers) to cut off ties in a family. I propose that it is most common for children to cut off ties with their parents, less common for them to cut off siblings, and least common of all for parents to cut off ties with their children—all for similar things (for example, narcissistic attitudes).
Why is this? I think it is likely due to one of two things—the first possibility that comes to mind is that is simply age. We have higher expectations for those who are, supposedly, wiser and have more experience. On the other hand, there might be a biological just-so story about it actually being about investment. We have the least investment in our parents (having received their investment instead), a moderate amount in our siblings, and the most in our children. This is a mixture of the resources we actually put forth towards that individual, as well as the expected future value of a good relationship with them (which is, currently, time bounded by mortality or at least years of useful life ahead).
Finally, when looking at the idea of a 'passive' love of family, it is more common than it should be to love a parent, or a child, and not have that love reciprocated—but we don't say our love for them isn't real. It seems like the relationship is intrinsically active in most cases. The only case that meets the passive equivalent that I know of is when we speak of (for example) loving a child you gave up for adoption that doesn't know about you.
Friend
I believe that friendship is the most complicated and most important of loves, and I struggle to contain the value of it in short. I have a compilation of some of the greatest quotes on it elsewhere, but I will attempt to summarize my thoughts here.
I think that friendship is the essence of a fulfilling connection with another person, mind to mind. If I was a spiritual man I might say spirit to spirit. I think that much of what we consider to be romantic love (addressed below, in slight) comes down to friendship that people have insensibly locked to only certain people.
Friendship is a ruler to measure by, a mirror to see the world by. Friendship is a spice that gives flavor to the blandest of foods and a lens that brightens the dullest of sights. Friendship can make days into seconds, can make seconds into days. Friendship builds and destroys countries, creates fortunes, and carves memories into the world.