WordNet getting depth of hypernymy

I'm quite new to WordNet. I need some help understanding the structure of WordNet. Currently, I used the MIT JWI WordNet package to implement my system.

So far, I am able to retrieve the synsets and hypernymy of a word. My question is: is there a way to retrieve the next level of hypernymy in the WordNet?

For example: the word "dog" has hypernyms of "canine" and "canid" (first level). How can I extract the second level hypernym which is "carnivore"? And then the next. Is this possible using the JWI?

I want to find the depth of the words according to this paper.

I hope I understand the paper right and I explain it right here as well.

Please someone help to clarify. Thanks.

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A WordNet word can have many senses, which means different meanings of the object. As an example, when we type "canine" as a query into the WordNet browser, we can see the noun has 2 senses: "canine tooth" and "canine" (as in the animal itself).

Therefore, in the first level, we can obtain some hypernyms but when we go up to another levels, I think we need to identify which "sense" of the word we are talking about. In particular, what if a word w has 1st level hypernyms A and B. A actually has 5 senses. Then which sense of it will we choose to use to go up and find 2nd level hypernym ? Similar for B too.

So I think in summary it goes down to which senses are you interested in, then you can go up and do the counting.

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