If you walk down into the Kendall Square subway station in Cambridge, Massachusetts, through the turnstiles and past the Paul Matisse art installation, you will see a common feature of all subways: a map.

If you have ever used a subway map, you know that they are not quite like other maps, which tend to be concerned with details like distance and terrain. Subway maps leave all that out, showing you the bare minimum you need to know to get from one place to another: which stations are connected to each other.

When you're using a subway, it doesn't matter how long a stretch of track is, what exact direction it goes in, or even whether it is above ground, underground, or under water. All you have to do is get on at one station and get off at another, possibly with some transfers between the two. Such a map is an excellent example of the types of networks used by network scientists.

In network science, a network is simply a set of things and the connections between them. The things are called nodes, and the connections are called edges. Nodes are really just placeholders for any type of thing that can have a connection or relationship, such as subway stations, people, or atoms. Similarly, edges are placeholders for connections or relationships, such as subway tracks, friendships, or molecular bonds. Just like the subway map, representing a system as a network strips away a lot of information, making it possible to focus just on the structure.

Networks are often visualized by drawing a dot or circle for each node and a line for each edge, as in the following diagram:

Looking at the network in this diagram, you might as yourself where to draw the nodes. The answer is wherever you want! (Although technically possible, it might be advisable to avoid hot surfaces, the mouths of large predatory animals, and/or important historical documents.) Because networks are meant to focus on structure and connectivity, there are many ways to draw the same network. Nodes can be drawn anywhere. Edges can be straight or squiggly, long or short. Edges can even cross, but that should never be interpreted as being connected to each other!

The same network can be drawn in many other ways, as shown in the following diagram. The nodes have been labelled with letters to make it easier to compare between different network diagrams. Regardless of which diagram you look at, any particular node will be connected to the same set of other nodes. While different ways of drawing the same network are equally correct, some may be helpful at highlighting particular features of the network. Chapter 11, Visualization, describes common approaches to visualizing networks and their various applications: