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At a first glance it seems to be obvious/expectable (at least to some extent) that the more frequently a word is used in language the more synonyms it should have.

Can somebody point out whether this has been proved scientifically/statistically and works/publications some data on this?

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    I think this could be tricky, because synonymy is usually gradient. However, the data are certainly out there: for English, you could get some kind of 'semantic neighborhood' score from WordNet, and a frequency score from various corpora (COCA, etc.). – Jeremy Needle Dec 3 '13 at 16:09

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