Goodbye Tree

I actually bought a real tree this season, thanks to an enthusiastic and inspirational friend who reminded me how great real trees are. Though nothing fancy, my tree was sized just right for my living room, beautifully proportioned, and smelled fantastic. I kind of forgot to water my tree after I set it up, and it spent most of the holiday season stubbornly refusing to drink my belated watering. But thankfully, it was rather stubborn about holding onto its needles as well. I guess you could say it fit right in.

Dragging the tree outside was another story. I sadly let it go at the curb and turned around to see a spectacularly messy trail of needles leading me back to my living room. That's all swept up now, except for a few lingering stowaways that I'm sure to discover in some nostalgic moment of 2005.

Christmas trees are perhaps my most favorite and special of all trees. But conveniently enough for this essay, a tree is also a special kind of network beloved by network analysts. (Keep reading, you non-mathematicians. I promise this will go down easy.)

To a network analyst, a "tree" is kind of like a family tree, only simpler. Here is a complete definition of "tree" that I find rather poetic: A tree is a network where every pair of nodes is connected by exactly one path. A good real-world example of a tree is a military-style hierarchy. When we speak of the "chain of command" in this kind of regime, that makes sense only because there is precisely one path of supervisory relationships connecting any pair of individuals in the group.

Network analysts love trees for the same reason generals do. Whether you are designing algorithms for Mapquest or commanding an offensive strike in Falujah, it's very expedient to eliminate ambiguity in favor of unequivocal efficiency.

But here is a funny thing: As easy as it is to find next year's Christmas tree in your nearest woods, it is basically impossible to find social network trees occurring naturally. People have a powerful desire to connect however they see fit, and the hierarchies we observe are but convenient artifices of simplicity laid upon the glorious natural mess of it all.

I guess I lay down the philosophy a little thick when it's past my bed time.

Happy New Year!