I have created a PPI network, now I want to compare it with random networks. I can generate the random network. In general, I am interested in the comparision plots of (i) degree vs betweenness centrality and (ii) degree vs closeness centrality and applying z-test to observe the significance.
Beside the network invariants you are interested into, the basic point is to find a plausible (in the sense of the particular hypothesis you want to test) way for creating 'random' networks. In this case (analogously with what is done with monodimensional signals) you must check if the actual value of the PPI network you observed is within the confidence interval of the random network population (usually 30 random replicas are sufficient given 30 is the minimum number that assures you the variables (in this case network descriptors) have a Gaussian sample distribution).
So the point is 'how to randomize original PPI' ? From your words it is not so clear what you want to do, if you want to check the relation between degree and centrality this implies you must have more than one REAL PPI with different values of both degree and centrality (otherwise you cannot compute this relation for real PPI so to compare how this changes with respect to the analogous plot for random networks).
Otherwise you can keep fixed the average degree of random copies and simply reshuffle who is connected with whom (i.e. the degree of each node) . At this point you can check if the betweness and closeness centralityy FOR THAT PARTICULAR DEGREE of PPI are within or outside confidence interval. (this kind of shuffling is anlaogous to change the temporal order of the values of a signal by chance so keeping invariant only the order-independent statistical prioperties like mean and sd).
Or you can keep fixed not only the average degree of the network but even the distribution of degree across the nodes , in this case the shuffled copies will correspond to the same original PPI network in wich each node has the same number of edges but with different partners. This kind of shuffling corresponds to the shuffling of a signal keeping invariant its Fourier spectrum, it is much les 'destructive than the other').
On the other hand you can adopt a more theroreticala ttitude and generate 30 'scale-free' networks with the same average degree than PPI and see what happens..this last proposal it is, in my opinion, much less interesting than the other two (see attached paper).
My modeled interactome does not follow power law degree distributions. Is there something wrong? If I remove some nodes then it follows power law. How can I justify this
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