Compare the degree distribution of a real networks and multiple random networks

Before the paper real world networks are rarely scale free, studies used to (still do) check for the slope in degree distribution graphs and if the slope fell between 2 and 3, discern that the network is a real world network. The slope of my networks are not between 2 and 3, and so I decided to conduct a Kolmogorov-Smirnov test (KS test) to check if there is a significant change in the degree distributions of my network and random networks (my network is bipartite and hence I used the sample.bipartite function in R to create the random networks) I created with the same number of nodes and edges.

Eventhough I created a set of 500 random networks, KS test being a two sample test, I could only test the degree distribution of my network against one random network at a time. The problem is that the KS test gives me different answers (significant and not significant) for the same network when I compare it with different random network degree distributions from the 500 that I generated.

Is there a possibility to compare the degree distribution of my real world network with the degree distribution of all 500 random networks rather than get differing answers comparing one at a time? I read that Kruskal- Wallace test might be able to do this but I don't know if that's true.

I use graphpad PRISM for my stats analysis and my R is rusty, so please give me a test I can use on PRISM along with an example if possible. Thank you for your help in advance.

Or am I doing the whole thing wrong and KS test cannot be used to compare the distributions between two networks. Any ideas are gladly welcomed.

• Not that I have enough rep to start a bounty but I have no choice. Please consider upvoting the question. – The Last Word Dec 3 '18 at 1:34
• Why not simply looking at the whole distribution of the slope coefficient across the 500 generated networks, which would give you the sampling distribution for the slope coefficient for random bipartite graphs of the same size (in terms of nodes and edges) as your actual graph. You could then look where the slope coefficient of your graph falls in that distribution. – baruuum Dec 9 '18 at 5:53
• @baruuum I am sorry but what do you mean by slope coefficient? The slope value? – The Last Word Dec 10 '18 at 18:11
• Yes, the slope in the degree distribution graph. If you plot the slope for the randomly generated networks, you get a distribution of what to expect in a random network; so comparing your actual slope to it, you can tell whether or how much your network (in terms of degree distribution) deviates from that random scenario. – baruuum Dec 10 '18 at 19:29