How do the connections relate to the root query?

I'm using the Graph via the API. And I understand how the depth 0 nodes are statistically significant to my query. However, I'm trying to understand how the connections work.

Are connections based on the global relationship between two terms? Noting that Bach and Handel are globally highly related. Or are connections scoped to the root query that generated depth 0 terms? Perhaps, as an example, noting that for Beatles fans a particular affinity between British and US Blues bands?

The depth 0 terms are essentially a list of terms. At this point we have no graph. We then use the depth 0 terms as a query to discover related depth 1 terms and use aggregations to group the new depth 1 terms under the depth 0 terms to derive the edges. The root query is essentially used just to get the ball rolling but you can also supply a guiding query to the API to help keep the exploration on track eg ensuring subsequent exploration is only considering recent docs.