I would like to compare network structures for two groups that formed on the same topic but for different reasons. I hypothesize that there will be differences in density and network centralization, but it is the case for both random and empirical networks to differ in these values anyway if they are of different sizes.
One possible solution is bootstrapping subgraphs, but I wonder if there are others that have a stronger theoretical basis for network studies?
I'm not sure how wise it is to try and "control for" size since it is such a crucial aspect of the processes that generate the detailed structure of a network. Just taking density as an example, the definition is the number of observed ties divided by the number of possible ties -- N(N - 1), so size is inherent in the definition.
More substanttively, the definition of density also makes it the probability that any potential tie will actually be observed. If that probability is the same in both a smaller and a larger network, the only way that can happen is if the people in the larger network generate more ties per person, which is another important influence on structure.
My recommendation is that in generating hypotheses, you begin with the substantive differences between the two settings and talk about how that those will be related to basic structural features such as network size and number of ties per person, and then generate more specific hypotheses about things like centralization, based on considering both substantive and basic structural features of the networks.
Thanks David. Indeed, I do have hypotheses based on the relationships between network size and centralization. However, one of the realities of the two related networks is that one is theoretical and empirically expected to be larger than the other. More specifically, I am examining social movements responding to historical dramatic events versus social movements responding to government announcements on the same policy issue / arena. So, size is a given but (relative) structure in terms of density and centralization is important (eg. i might expect more conversation, debate etc. for the latter group).
Perhaps the answer is in examining the number, size, density & centralization of strongly connected components or some other theoretically important substructure?
Thanks for the reference, Victor. I did find some articles that were helpful for theory development.
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