Graph Traversal

Here is your task:

Create a graph with 30 nodes ( => connectivity matrix). Since the connectivity matrix is empty (zeros everywhere), you have a maximally disconnected graph: all nodes are single nodes.
While the graph is disconnected, add single random bidirectional connections.
Print the connectivity matrix (good old ASCII style, 30 rows, 30 columns), for every connection, print the depth relative to node one. This means: instead of printing '1' for 'connected', print the depth value.

You are at the end of the semester now, you are therefore experienced and grown up JAVA programmers! I therefore won't give any further hints, except if required (come to my office / email for help).

Ok, a little help. You need a method to traverse the graph. Start from node one, and mark every node (keep an array for the nodes) which was visited. After traversal, check the array: if not all nodes are marked, your graph is still disconnected.

Bonus (4 points):
Visualize the resulting graph as a circle of 30 nodes, with edges between connected nodes.

Bonus (another 2 points):
Same as above, but show the graph each time a single connection was created (and pause for 100 milli seconds).

Bonus (another 5 points):
Program an ANIMATED little box that travels (depth first)the graph along the edges. Visited nodes should get a different color.

Due date: Sunday, May 2