I am curious if there has been research on a topic I'll describe in the next paragraph.
The topic: Suppose that we have an English dictionary and a huge piece of blank paper. For every entry in the dictionary, we draw a circle and label it with the word defined in the entry. Then, for every entry in the dictionary, we draw an arrow from the circle labeled with the word defined in the entry to all words which appear in the definition.
For example, the online Merriam-Webster entry for snobbish defines the word as "being, characteristic of, or befitting a snob." For this entry, we woul draw seven arrows from the circle for snobbish circle to the circles for being, characterstic, of, or, befitting, a, and snob. (Perhaps we may need to take account of inflections -- e.g., if snobbishly appears in another word's definition, we could draw the line to snobbish, since snobbishly isn't an entry on its own in Merriam Webster. But I imagine that we can work out sensible alternatives for challenges of this sort).
The interest, in abstract: I would love to see if what the overall picture ends up looking like, what words have a lot of arrows coming in, how the choice of dictionaries changes the patterns, what insights scholars have been able to gather, etc.
My interest is admittedly general and vague, so I will rephrase my question to be more concrete:
The question, in concrete: Has there been research on this topic? If so, what is the name of the area of English or linguistics which covers the topic (so that I may look up further)?
Potential answers might look like:
- Area A is the field in linguistics which would delve into a topic like this. Visit this link.
- Person P has made visualizations you describe. See this picture. Visit this link.
- Area A is the field in English which would look into a topic like this, but as an academician in the field, I am not aware of this type of research done seriously.
What I've tried: I used search engines with some combination of terms like "dictionary", "define", "graph", "cycle" (e.g., "english dictionary words defined in terms of words" and "dictionary entries into directed graphs"), but found nothing which seems to cover the topic. (It doesn't seem to help that if I use the word "graph", "dictionary" is almost always interpreted as a synonym for associative array, not a book of definitions for natural language vocabulary...).
I did find two entries from Stack Exchange sites which cover related but ultimately different questions -- one asking if there is a set of words which can define all words (which could be rephrased to a question about whether the graph has a set of nodes whose outgoing edges are contained within the set -- though, if phrased this way, the set of all nodes trivally satisfies the conditions) and another which is more philosophical.