Has there been research on how things look if we represent a dictionary as a graph of nodes from entry words to words appearing in the definitions?

Question

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.

Answer 1

Not exactly what you’re looking for, but WordNet is prominent academic resource related to your interests, and has seen applications in all sorts of research and even things like natural language processing technology.

Here’s how it describes itself (emphasis mine, to show relations to your interest):

WordNet® is a large lexical database of English. Nouns, verbs, adjectives and adverbs are grouped into sets of cognitive synonyms (synsets), each expressing a distinct concept. Synsets are interlinked by means of conceptual-semantic and lexical relations. The resulting network of meaningfully related words and concepts can be navigated with the browser(link is external). WordNet is also freely and publicly available for download. WordNet's structure makes it a useful tool for computational linguistics and natural language processing.

WordNet superficially resembles a thesaurus, in that it groups words together based on their meanings. However, there are some important distinctions. First, WordNet interlinks not just word forms—strings of letters—but specific senses of words. As a result, words that are found in close proximity to one another in the network are semantically disambiguated. Second, WordNet labels the semantic relations among words, whereas the groupings of words in a thesaurus does not follow any explicit pattern other than meaning similarity.

I haven’t looked, but the site may discuss specific research programs, papers, or applications which incorporate it, and any insights they have surfaced (as you asked). If not, searching for citations to WordNet certainly would.

Note: the entire database also publicly and freely available for download, if you want to do your own analyses or just play with it.

Answer 2

• There are many academic domains which might apply here:
  • Lexical semantics (word meanings and their features relations) and specifically lexicography (making dictionaries). Covers things like semantic features, grading, hyponyms and meronyms.
  • Epistemology, specifically the theory of definitions. This covers ideas like the difference between stipulative (technical, forced meanings) and descriptive ones.
  • Database theory (in computer science) and the idea of knowledge bases and ontologies. Describes how concepts (not words, but how concepts are related (words point to concepts). WordNet is a good implementation for English.
  • Graph visualization. Graphs can get pretty big pretty quickly and then very hard to read, so there is a lot of research in figuring out how to display graphs well for readability.
• In practice
  • Most on-line dictionaries and thesauruses provide a very limited implementation of what you seek, links to other entries in a word's entry. For example, Wikipedia style allows links to other Wikipedia entries, but there's no automatic generation of a link for every word in an entry.
  • Visual Thesaurus gives the synonymous 'neighbors' of a word visually, but then so does Thesaurus.com in a less graphical form. These aren't exactly what you're looking for but are nearby. WordNet goes well beyond just synonyms but is less a practical thing than a high powered implementation tool.

The idea you give is a very productive one having lots of implications. A basic philosophical problem is if one word is defined in terms of others, what does the graph of words, connected with 'is used in a definition of', look like? Where does it stop? Are there things that are at the bottom that are not defined in terms of other things? Or is it turtles all the way down? Are there things at the top? (or is that really the bottom) They say you shouldn't define something in terms of itself, but what about two things in terms of each other? What about a cycle of 3? What's the longest cycle? So many questions!

A lot depends on how you 'do' your dictionary. If you just take a dictionary and put in links for every word, there's no bottom (the word 'the' will have a definition in words... it may not use the word 'the' but it actually may. But either way there will definitely be cycles and most likely 'top' words (word that aren't used in other definitions. If you don't use any 'stopwords' (like prepositions and connectors, then the structure is different, but rally depends on the definition composition style of the lexicographer.

Follow the links. You're not alone. If you find an online dictionary that links -every- word in the entry then add/comment here.