A useful way to represent networks is to imagine the nodes as dots and the connections as line segments, which we will also call edges. This network diagram can give us a glimpse into its structure. So what will the network of friendships look like in Regulartown? At some point it may look something like this:
Each person will try to find their four friends, and as new people move to town, they will look for someone with fewer than four friends to connect with. In this way the network will continue to grow over time, continually expanding at the edges as new nodes are added. (It’s also possible for independent cliques to form, but we’ll ignore that possibility in our example.)
Diagrams of networks can be illuminating when they indicate a clear structure. But when networks get big, or don’t exhibit the kind of regular structure of a Regulartown, diagrams may be less useful. It helps to develop different ways to analyze a network’s structure. One way is to think about the degree distribution of the network.