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What base does vocabulary.com use for its hierarchy of meanings of a word? For example see http://www.vocabulary.com/dictionary/sound. Are top levels (numbered list) all homonyms?
What structure do you think is best for showing various meanings of a graph (word) in a dictionary?
Vocabulary.com's senses (and entries) are generally the same as WordNet's: compare with sound at wordnet.princeton.edu. Vocabulary.com has clearly done some filtering to make the entries less Weirdnet: note that there's no example sentence for "the audible part of a transmitted signal", which in WordNet is exemplified by "they always raise the audio for commercials", i.e. without the headword "sound".
That's a much more straightforward question than what is the best structure for showing the various meanings of a term in a dictionary. As Alex B. notes in his comment, it depends on the dictionary, but this question asks about meaning as "hierarchical", which could be considered begging the question. Most synchronic dictionaries do present meanings within an ad-hoc hierarchy, but there are also componential and prototypal approaches to semantic analysis/description, very solidly exemplified in Pustejovsky's Generative Lexicon theory.
