Help with Graphs (BFS mostly)

Okay so I posted a thread about my project before, how I need to create generated word ladders and all that. Now I am to the point where I need to create a method which will find the shortests path between a start word and an end word. For example:

startWord: Head
endWord: Feet

And then a wordLadder would be something like...

Head, Heat, Feat, Feet,

Now I know that I am expected to use a graph here, and I was suggested to use a Breath First Search as I believe this works between two points or something along those lines. Expect I am not sure how to use this with my program. Here is my current code to give you guys an idea of how I made the program so far.

I've bolded and put the discover method in Italic to make sure it stands out more than the other methods, easier to read hopefully...

Depending if I cant understand graphs in the next hour or not, I may be able to edit in my other problems I am having, otherwise explaining to to use BFS Graphs would be brilliant, especially in this example.

I'm glad to see that you're making some progress on your homework assignment from what you originally showed us four days ago on the thread titled "Trouble with Iterators and Hashtables (Java)". But it looks very much like you're posting homework problems to the "Programming" forum rather than to the "Homework & Coursework Questions" forum. That makes it much less likely that we're going to spend much time trying to understand your code and help you help you complete your assignments.

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Would it be possible if this thread could be moved over to there then at all please? Or would I be better off creating a new thread these since I have more problems with my code now...

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Please create a new thread. Thanks.