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I was wondering if anyone has ever studied the graph where vertices correspond to words of a language and there is an edge between two vertices if and only if there is a word association between the corresponding words. I want to know which (random) graph model would be a good approximation (so I'm mostly interested in the quantitative properties like the average degree or the clustering coefficient). The results for English language are preferable but ultimately I'd be happy with anything.

Regarding motivation, I've been thinking about word association games lately (particularly Codenames). In the simplest mathematical model I can think of we have a graph described above so to have any meaningful results I need a good model. Of course, if you're aware of any research of this kind please let me know.

I was inspired by this question.

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    "Word association" is not a very well-defined concept. Certainly not well enough to support a graph-theoretic formalization. Might work with a decent definition of "word association" (is the association, for instance, semantic, phonological, scatological, or what?), some boundary examples, and some reason to assume everybody has the same sets of associations for every word. – jlawler Jan 13 '18 at 22:21
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    Hmm, this reminds me a bit of Visual Thesaurus – brass tacks Jan 13 '18 at 22:29
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    @jlawler suppose we simply go with semantic association. Then we can probably asuume that people indeed have similar sets of associations. It is also the most common type in those games. – Petr Naryshkin Jan 13 '18 at 22:53
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    "Semantic association" is equally vague, unfortunately. And all evidence points to vast individual differences in meanng and therefore associations. – jlawler Jan 14 '18 at 0:50
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    @jlawler it still feels to me like we can safely ignore individual variations and consider only the most obvious association ("chicken" -- "egg"). Imagine you're playing a game of this type with people you don't know. Then you're going to (try to) use only some kind of universal associations. In any case, could you perhaps point me to the relevant literature ("all evidence")? It may help me. Besides, those observations sound pretty interesting on their own ;) – Petr Naryshkin Jan 14 '18 at 13:47
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There are language resources called wordnets that represent graphs of hypernymy and hyponymy and synsets. The prototypical example of such a resource is the Princeton WordNet for the English language that is available under a free licence.

There is another type of language resource called ontology. Typically, ontologies are constructed for particular domains of knowledge.

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