Studying the structure of existing friendships in your community can help you forge the best connections when forming a new circle of friends.
When you start at a new school or job, or move to a new city, how do you go about making new friends? You could take an active approach, forging strategic connections with the popular kids and the movers and shakers. Or you could leave things to chance, relying on random groupings and associations. Whatever your approach, understanding the structure of existing friendships in your new community can help you make the best connections, which will ultimately define your circle of friends.
Imagine moving to a strange new city, Regulartown, that has a strange rule: Everyone can have at most four friends, and everyone wants to maximize their friendships. What will the structure of friendships in Regulartown look like? To explore this question, we’ll use a mathematical object called a network.
Simply put, a network is a set of objects, called “nodes,” and the connections between them. Networks are mathematically versatile: They can represent computers and the wires that connect them, authors and their collaborations, or the states of a Rubik’s cube and the moves that transform them — essentially any set of connections, real or abstract. To study friendships in Regulartown, we’ll create a network where the nodes are people and the connections are the friendships between them.