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What, Exactly, is a Small-World Graph?
How a Simple Mathematical Model Can Lead to Massive Results!
I’ve been writing a lot about mathematical graphs recently. That’s because these objects are fun to study and have so many applications! In this article, I’m going to talk about a very special type of graph called a small-world graph. If you’ve read any of my recent articles, then you know I’m not talking about the common graph with the x and y axes. Instead, I’m talking about structures with nodes (points) and edges (lines) connecting them.
Now, graphs can be used to model all sorts of real-life things. Last week, I wrote about how a graph can represent a map of a region that is divided up into smaller parts, like the United States. That model led to its own variety of interesting results, and if you want to read it, it’s linked at the end of this article.
Graphs can also be used to model information and social networks. You could imagine a graph where each person is represented by a node and two people that know each other are connected with an edge. These two people have a distance of 1. In the example graph above, pairs of nodes with a distance of 1 would…
