Connedted graph task

Has anyone had good experiences with any Java libraries for Graph algorithms ?

To clarify, I'm not looking for a library that produces graphs/charts, I'm

looking for one that helps with Graph of ( characters ) .

I want to design a test task that the user should try to connect characters

by order . For example connect (1) to (2) then (2) to (3) . can you suggest what should I use for this ?