I am trying to come up with a way to statistically test this question, and could use some input, as it's far afield from what I normally do. I have a hierarchical network, like this one:
And a centrality measurement of each node. What I want to do is test if the measurement for each "layer" (i.e. nodes 1 step from the diamonds, or 2 steps from the diamonds, etc) are uniformly distributed. The problem is that the layers aren't actually independent - the layers closer to the diamond will inherit some of the distortions from the layers below them, so what I actually want to test is that the distribution for layer X is no more distorted than the layer before it.
Any ideas how to go about that?