(Note to authors: Edit this document not in the wiki, but rather in the graph, at :JwGnhoHw23PfCIyp:.)
Sometimes things need to be used together. We would like them to be found in the same place, or at least close to each other. A graph makes that easier.
The diameter of a circle is the maximum distance between pairs of points on it. Most pairs of points on the circle are closer to each other than the diameter, but nowhere on the circle is farther than that from anywhere else on the circle.
For knowledge we can define a similar concept, the "relevance diameter": the maximum distance between pieces of information that are relevant to each other -- the kind we wish were found near each other. A small relevance diameter is good, because we never have to travel farther than the relevance diameter in order to find something we need.
The diameter of a graph can be smaller than it can be in a tree of the same number of things. That's because in a graph, anything can be connected to anything. If it takes too many hops to get from A to B, you can just add a connection from A to B, and now they are one hop apart.
You might imagine that this could lead a writer to draw so many connections to something that they became hard to choose between. However, connections to something can be grouped, which lets the number of connections to it stay small. This is just like managing a folder in a file tree: If a folder has too much stuff, you can divide it into subfolders, and it becomes easier to read.