To discover new thought relationships and ideas, allow for boolean operators with the graph and search in general. I can imagine combining a couple filters with two or three significant words all using the “OR” boolean operator. For example, city OR food OR parks OR #food OR #music has three terms, and two tags. That would result in a graph for cards with all those terms and filters. This type of search is currently not possible. AND, NOT, OR , and ( ) operations should be implemented.
To expand on the first search, imagine doing a second boolean search and adding it to the results of the first boolean search. The resulting graph would have two hemispheres of information, with some overlapping connections. With a third boolean search, and a fourth, etc., a new knowledge graph would grow based on the boolean searches. Selecting one of the boolean search strings would highlight the corresponding portion of the graph as a visual cue. The highlighted potion might look like glowing neurons when in dark mode.
(A boolean feature request has not been made yet, although @Tobias mentioned it in passing in the Thoughts and Feedback section a while back.)
To further refine a search, allow for a graph or search to display nodes or cards from within a selection of multiple parent cards (inclusive of their child cards) to the exclusion of other parent cards. On MacOS, for example, one could select multiple parent cards in the outline with the command key. This describes a different search feature, so I’ll make a separate request for simplicity.
Lastly, how does the graph work for people that organize mainly by tags and links? I believe there are a few Supernotes users that organize this way. (Since I prioritize organizing via parent and child cards with a fair number of links but just a few tags, maybe others can chime in who organize primarily via tags and links.) I just made a new feature request for tags as nodes.