Edwards (1995) describes a stepwise, backward-elimination model selection method which starts from the saturated model and removes successively the least significant edge (pairwise association).
The applet shows the graph for these data at the initial step, before any edges are removed. The edge distances are proportional to the p-value for each edge. (David, p.24). [It's not clear that this is the best metric.] Drag a node around, or click a button, and watch it find a stable configuration reflecting those distances. Press the Scramble button to move the nodes to a new random configuration. Then, try the next stage, after removing the least-significant edges.