This applet allows you to do a Breadth Search First on any graph (not a multigraph). It has a text area on the top right corner which display pretty much all the info you need.
Here are a few instructions you might find useful:
To create a vertex: Click on the screen. They are represented with a Red Square with a letter on the top. Just in case that you need to click, if you drag it will not add a vertex.
To create an Edge: Click on two vertices and a red line will be drawn between the two vertices which represents and edge.
Now once you have the whole graph, there are two modes the program can find the path, if you hit enter it will give you the answer right away, but if you want to step through just hit the "S" key to step until it is done and as you hit the s you will se how the algorithm is calculating the distance of each vertex from the starting point.
if you have any question e-mail me at: czambran@mum.edu