Consider the graph $G$ whose vertices are MO questions and edges are links between the questions. What does $G$ look like?
I'm happy to define a "link" in the same way the SE software seems to -- if a hyperlink to Question A is written anywhere in the text of Question B or its answers, or the comments to either Question B or its answers, then Question A will pop up in the "Linked Questions" sidebar on Question B, and also Question B will pop up in the "Linked Questions" sidebar on Question A (the graph is undirected).
$G$ is very far from connected. It has many nodes (perhaps the majority?) with no edges at all.
What is the largest connected component of $G$? Are the component sizes distributed according to a power law or something?
What is the maximum degree of a node in $G$? How are the degrees of nodes distributed?
How does this graph structure compare to the tag structure or the user structure (I'm not sure of the best way to make this question precise)?
What happens if we add to $G$ nodes for arxiv preprints or journal articles and links from MO questions to them?
I think that studying the structure of $G$ will not shed as much light on the structure of MO as, say, studying the link structure of the Internet as a whole sheds on the Internet, since links as defined here are not the only way questions can be related. But it still seems interesting.
Probably these sorts of questions have been considered thoroughly by the developers at SE, as the structure of $G$ is presumably an important ingredient in generating the "Related Questions" sidebar.