“In 1999 […] Barabasi and […] Albert proposed that a particular growing process for networks, which they called preferential attachment, is the explanation for the existence of most (if not all) scale-free networks in the real world. The idea is that networks grow in such a way that nodes with higher degree receive more new links than nodes with lower degree. Intuitively this makes sense. People with many friends tend to meet more new people and thus make more new friends than people with few friends.” – Melanie Mitchel, Complexity: A Guided Tour
Alright–so I started with dessert with that quote. Couple things I need to bold word.
What the fuck is a scale-free network?
There are four main properties that define this network structure that I am ripping off from this amazing book I read and I am adding my own words to attract an educated mate.
Ok. So you are totally at a party, and everyone did some party drug that makes them point to the person in the room that they want to tag themselves with on facebook the most. A scale free network has a hierachical structure, meaning that a collected few are getting pointed at the most. Every finger pointed at an individual, in graph theory, would be called an edge. Or a link. These are just words used to establish a said relationship amongst a bunch of nodes (party people, in this case.)
But a small amount of people, in a scale free network, have a large amount of fingers pointed at them. The sum of all the fingers pointed at an individual would be refered to how many ‘degrees’ the person (node) has.
“1) a relatively small number of very high-degree nodes (hubs)”
But its a really big party. So within the small group of people that are getting the most amount of fingers pointed at them, there is a wide range of values as to HOW MANY fingers are pointed at the special people. So amongst the special people, there is wide degree of separation as to how special, how much influencce, a person has.
“2) nodes with degrees over a very large range of different values”
At this amazingly large party where people are acting upon a relatively fixed impulse (making this example much more pleasant and less chaotic and, you know, less realistic) a self-similiarity would emerge. There would be a shape that, through a series of repeated drawings, would trace the scene. We know that the points relate with each other, meaning at the very least we could use lines–but if there is a dominant set of ‘shoulds’ the room follows and other nodes emulate, the repeated pattern could be much more intricate and ‘woahman.’
“3) self-similarity”
Scale-free networks also have a feature called the ‘small-world’ property, more unanimously introduced as the Kevin Bacon game. Meaning that, within this huge party, it would be possible to find similar friends with a person we have never met before in a small number of steps. We would chink glasses, go “OMG YOU KNOW CAPTAIN MORGAN,” and cheerifully declare “IT’S A SMALL WORLD!”
Sorry that’s a little absurd and I apologize–just think the Kevin Bacon game.
“4) the small-world property”
Scale-free Networks have power-law degree distribution. That has a lot of implications and tie ins with fractal geometry.
But anyways, I believe preferential treatment arises due two factors–a small group of people looking to perpetuate a certain way of seeing, and a large group of people looking to emulate how they ‘should’ behave. These drives leverage each other.
isomorphis 