Love and Mathematics
A Directed Cyclic Graph is a data structure which describes the relationships (called edges or vectors) between things (nodes, points or vertices) in a way which makes them representable and computable. We can even draw these graphs using circles, arrows and text to illustrate relationships, consider the following:
Already we have a critical problem, English overloads "Love" with both the romantic ("eros" in Greek, "kāmo" in Pali) or possessive form, as well as the more "Pure" altruistic senses ("agápe", "philía" & c. in Greek, "metta" & c. in Pali). Within the philosophy of Buddhism, originally recorded in Pali, and maintained across South East Asia in its successor linguistic traditions the two are generally separated into Love, in the Metta sense, and Desire, in the Kāmo sense.
In order to represent these in our graph, we need to label our edges with (M) for Metta or "Pure" love and (K) for Kamo or Desire:
That's a little better but it understates just how different these forms of Love and Desire are in their lived experience and in our popular conception, and it doesn't clearly draw the bright line that exists in the Dharma between the two and how they are addressed. But we can now look at some less ideal relational graphs with some clarity: 
Now, we could continue in this vein for some time, the variety of difficult and dysfunctional relationships rapidly approaches infinity as you add nodes to the graph. If we wanted a catalogue of human misery we'd be reviewing the latest DSM. What we are looking for, is a way to better understand and navigate our love lives, what we want to gain is the key insight into making better relationships.
Modern Romance
Familial relationships are wonderful and deep, but to get there you have to first negotiate a romantic relationship, which can be a challenge, especially for people who look at it as a negotiation to begin with.
Our notion of romantic relationships are heavily skewed by our media environment, in fact the very concept may be a cultural construct, with historians tracing the emergence of courtly love and the "game of love" to the Middle Ages. While the strength of romantic feelings and of sexual attraction are present in some of the oldest human writings, going back to the Song of Songs, still preserved in nearly all modern Christian bibles (my go-to reading if I'm temporarily inconvenienced in a pew for some family or friends service).
In our shared media we see a preference for romantic Intensity vs Quality, preferring strong feeling, in an addictive desire for the rush of falling in love. Oxytocin is a hell of a drug. This is not just misuse of sexuality, but probably also abuse of intoxicants; and it's one of the most challenging temptations in our lives.
ROMANTIC LOVE WAS INVENTED TO MANIPULATE WOMEN
We are directed to focus on the Magical Attraction of the "Prefect One"; and, once so attracted, testing our intended partners rejection tolerance and eventually pushing them to decision fatigue (sometimes referred to as the "Stalker Success Story" trope). This sort of persistence pays off in many a romantic comedy, and may reflect a positive survival value of our special human talent; persistence or endurance hunting. We are evolved stalkers and the displacement of this core evolutionary drive into our romantic lives helps explain both the romantic cross-connect and the very real problem of obsession and stalking.
The Game Theory of love suggests that we should be willing to make significant sacrifices in the name of our Attachment, especially considering The Love Cure[1] which will make us whole and heal our emotional wounds (sadly, it won't, and even more sadly those with similar wounds will tend to pair off because they can understand and empathize easily). Under this theory we must give up something of ourself to have a quality relationship, but the value that we gain is greater. While this gamble can pay off, often the investment reaps only bitter disappointment; sacrifices were made but the emotional interest never accrued.
Variable Misfits in Love
In his design-cult classic Notes on the Synthesis of Form, Christopher Alexander lays out a thesis of design organized around Misfit Variables: specific features which a successful design must not have in order to fully fit a purpose. He lays out the example of a teapot which must not: fail to hold sufficient water, fail to allow water to be heated, fail to keep heated water warn, burn the hand that picks it up, and so on. You know you have a good teapot when it lacks any of the features on your list.
Attachment Theory gives us four major types of attachment which we can use to model misfit variables for our potential romantic partners:
- Avoidant: looks away from love to protect a deep relational wound
- Anxious: projects an idealized image to cover their poor self image
- Fearful: craves affection but can't tolerate the loss of affection in relationships
- Insecure: self concerned and distressed by what they see as abandonment
The combined opposite of all of these is the Secure Type of Attachment. This secure type comes from exactly one alignment of forces: loving yourself. It means taking the time to look at your own relationship history and see where you have yourself played the Avoidant, Anxious, Fearful, and Insecure parts in turn. Some of us focus on one or the other, but we are all capable of feeling and expressing all those ways at any time.
It's not easy, it requires some self-discipline, it might mean being alone for a while, but if you want to try to build a really stable relationship, it's probably worth putting in the work, and understanding that the reward for that work is more work. Managing our relationship with ourselves is challenging, rising to meet that challenge is what makes us worthy to take on the work of relating with others.
Bizarre Love Triangles
Of course, ideals are just that; the map is not the territory and physics is just a model. We get into all kinds of less than idealized situations and this can have a devastating impact, triggering emotional regression and causing problems in our lives. Consider all the possible forms of love triangles you could be mixed up in:
In these situations, we can find ourselves deeply wounded, aching as though our hearts have been torn out. Desire, and particularly desire for love (even if our models are perfectly well understood and we totally get what's going on) cuts deep, and drives behavior we'd otherwise find hard to understand and wouldn't generally tolerate, consider Shakespeare's description in As you like it: Act 3 Scene 2:
ORLANDO: What were his marks?
ROSALIND, (as Ganymede): A lean cheek, which you have not; a blue eye and sunken, which you have not; an unquestionable spirit, which you have not; a beard neglected, which you have not[…] Then you hose should be unguarded, your bonnet unbounded, your sleeve unbuttoned, your shoe untied, and everything about you demonstrating a careless desolation.
This "careless desolation" implies a deep obsession, driving Orlando in the play to hang letters of love on a tree in an attempt to reach the object of this obsessive affection, but the object of that affection (here in disguise) expects a sacrifice: if you are truly in love with another you would cease to be able to love yourself, which would show up as negligent self care:
ROSALIND, (as Ganymede): But are you so much in love as your rhymes speak?
ORLANDO: Neither rhyme nor reason can express how much.
ROSALIND, (as Ganymede): Love is merely a madness, an I tell you, deserves as well a dark house and a whip as madmen do: and the reason why are are not so punished and cured is that this lunacy is so ordinary that the whippers are in love too.
So here we see a call for self-possession and also an admission that, and as much as we've come to understand ourselves, in aggregate, and developed theories about love; the lived experience is nothing like that. It's a form of madness we are all constantly having to forgive each other for experiancing.
When we talk about the process of "falling" in love, we imagine a situation in which we have no control, we can only flail about uselessly against gravity as it drags us down to our end. Having recently experienced this for the first time in a long time, I was struck by how apt that metaphor feels, particularly the moment you hit the ground.
Sign Off
And now, for all you lovers out there: Broken Social Scene, performing "Love and Mathematics" from Feel Good Lost[1] Sorry, not sorry
[2] Caution: tvtropes link