Your vault is a graph whether you plan it or not. Pages are nodes, wikilinks are edges. Every structural decision in the previous section was a decision about what shape that graph takes.
Four terms are enough to reason about it. This section is about your vault's own graph — wikilinks, shape, health. Graphs as an agent's memory in general (GraphRAG, extraction, stores) are the knowledge graphs handbook.
Degree is how many links a page has. In-degree is how many point at it, out-degree how many it points out. A page with zero in-degree is unreachable by following links, which is what makes orphans a problem rather than a cosmetic issue.
Path length is how many hops separate two pages. This is the one that matters for answers: the agent following links from a starting page can only reach what is a few hops away before the context budget runs out. Two related ideas eight hops apart will never be connected in an answer.
Clustering is how much a page's neighbours link to each other. High clustering means a genuine topic area. Low clustering with high degree usually means a page that collects unrelated things.
Components are the disconnected islands. A vault in five components is five vaults, and nothing in one will ever inform an answer about another.
The star. Everything links to two or three hub pages and to nothing else. Path length between any two leaves is short, but only through the hub, so the graph tells you nothing beyond "these are all in my vault". Usually caused by linking to broad concepts instead of specific ones.
The chain. Sources link to the concept they introduced and nothing links sideways. Common after a bulk import that ran without checking existing pages. The vault grows and never connects.
Islands. Distinct topic clusters with no bridges. Sometimes legitimate: your cooking notes and your database notes genuinely do not connect. Often not: two clusters about related things that were built under different vocabulary and never linked because the aliases were missing.
Dense within topics, sparse but present between them. Most pages reachable from most pages within three or four hops. Hubs that exist but do not dominate. A small number of bridge pages that connect clusters, which are usually your most valuable pages, because they hold the connections you could not have made from one source alone.
When you ask the vault something, the agent starts at the pages that match and walks outward. The graph is the search space. A well-shaped graph means the walk reaches the relevant material in a few hops; a badly shaped one means it either reaches nothing or reaches everything.
That is the whole argument for the linking rules. They are not tidiness, they are what determines whether retrieval works.