I'm probably going to be way behind the rest of you (I know nothing about Java) but I'd really like to come along for the ride, I think this is really the best way to learn.

Any thing I can do I will, I'm basically on the same boat as mikau on this one.

That is why I chose flash over java for the Math Is Fun website ... the average web user hates the wait. So if you are designing something to be popular use flash (and use swishmax to make it)

HOWEVER, while flash is great at animations and user presentation, it is painfully slow as a programming language (orders of magnitude slower than C++).

Here is an idea: have our program manipulate graphs in such a way that a display can be built on top of it.  Since most of the code for C++ and Java is similar except when it comes to graphics libraries, it will be easily portable into the other language.  Perhaps a general display class which can be written for any type of application, whether it be glut, Java applet, Swing, etc.

Does anyone have an objections to this project?

by that do you mean that we wont be writing a specific GUI to interface with the library, but rather simply create a library that is easily translatable and a GUI may be built for whatever purpose in the target language?

So the first question is, what do we want this program to be able to do?  Here are a few things that come to mind:

1. Represent graphs, multigraphs, trees, forests, weighted graphs, directed graphs, and weighted directed graphs.  This means accepting input and output.

2. Search for shortest path from any vertex a to another vertex b in any of the above.

3. Find a minimal spanning tree in a weighted graph.

4. Find a spanning tree in a graph.

I'll be adding to this later on.  Please enumerate everything you say, continuing off of mine.  In other words, the next person should start with 5.

6. Lay out in 2D with no or minimal crossings.