The search bar on top of Graph is not working in the same way than the search bar in Discover.
In Discover, it's acting as a filter, scoping down the things you look at. In Graph it's the other way around - if you search for things, you are adding them to the workspace.
As Graph is about searching for significant relationships, it's doing "hops":
The query is used as the "seed" to a crawl when you hit the search button. In the matching docs matching your query we pick the top N nodes (what you might call "hop 1" in the crawl. We then use those N nodes as a query to find further docs that may or may not match the original search query and the nodes they contain (this you might call hop 2). We can then draw lines between the nodes discovered in hop 1 and hop 2.
In your case, the documents matching your initial query contain e.g. the tag "Margin", and this tag is also present in document with another "Date of Note" (e.g. 2017-10-31) - that's the hop.
The underlying "explore" API (https://www.elastic.co/guide/en/elasticsearch/reference/current/graph-explore-api.html) powering the Graph interface does have the concept of a "guiding query" which is what you need here for scoping for exploration to documents before 2014, but unfortunately it's not exposed in the UI.
It is theoretically possible to paste the JSON of an explore API call into the search field and add the guiding query this way (you can copy the ones you used by clicking the "Inspect" button in the top row), but it's hairy to edit the JSON by hand in there.
If you are only ever looking at documents prior to 2014, you can also prepare an index pattern only containing the data you are interested in, then start a new Graph workspace based on that index pattern.