To Graph Or Not To Graph

Recently, I had an interesting conversation with an associate regarding graphs. My colleague had worked with someone who held the opinion that graphs were worthless, since anything you might decide based on a graph should really be decided based on a statistic. My initial response was to reject this idea. I have used graphs a number of times in my work, and believed them to be useful, although I readily admit that in many cases, a simple numeric measure or test could have been substituted, and may have added precision to the analysis. Data visualization and related technologies are all the rage at the moment, but I wonder (despite having a nerd's appetite for computer eye-candy) whether data mining should perhaps be moving away from these human-centric tools.

Thoughts?