“How Network Math Can Help You Make Friends”
Link to article: https://www.quantamagazine.org/how-network-math-can-help-you-make-friends-20180820/
The article comes from Quanta Magazine, which is one of my personal favorite sources for math/cs news. Quanta aims to publish interesting accomplishments in the fields of math, physics, computer science, and biology all while maintaining digestible, easy-to-read articles for the average arm-chair reader. The article “How Network Math Can Help You Make Friends” covers a wide range of probabilistic and deterministic generalizations of human friendship that are tied together under network theory.
Making friends can be hard, and it may sometimes seem that some individuals are just inherently better than others at accumulating “friendships.” But how can we maximize our friendship making chances so that we seem like one of the social elites. Furthermore, to what extent is the perception that some people are just much better at making friends true?
When friendship is random, the degree (number of friends) a node (person) has is well distributed–few individuals have an excess of friends, few have very few, most have around n friends. We can think about this as a binomial random variable. If making friends has a probability Pr(F) = 0.5 between all individuals then the odds of making friends with all 400 students in your networks class is (0.5)^(400) ~= 0–assuming independence. As we increase n toward infinity (or 7 billion individuals), we see that the distribution looks very normal. If you want to visualize this, look up Galton Board demos.
Clearly we have dispelled the myth of multi-modal friendship distributions when friendship is quais-random, but we know that there is a strong interdependence between nodes in a friendship graph. “Preferential attachment”–namely that “A node with many existing connections is more likely to get new connections than a node with few existing connections”–is the new buzz word to describe nonrandom friendship model trends. This idea has nicely shifted our beautiful Gaussian curve, into an ugly fat-tailed curve. Why does this tend to be? Recall the strong triadic closure principle. The more friends an individual has, the more possible instances of open triangles they have, which gives this closure principle more cases to impose itself on. Sure human behavior is much more complex, but simple ideas like preferential attachment and STC have a sizable effect on what happens in the network.
So if you are trying to make more friends, don’t get discouraged by other’s success. Maybe start with the low-hanging fruit and watch the interest accrue on your investment.