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I am working with social network data. I have multiple networks of various sizes and I'm calculating indegree (the number of connections between people) in each of the networks. I've been told to normalize the count of the number of connections by dividing by the number of possible connections for that network. I'm unsure whether this is accurate, but if it is, can I just work with a linear regression on this transformed data? If it's not accurate should I just go with the Poisson or Negative Binomial route? If someone can provide citations or proofs for reasons that would be greatly appreciated

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    $\begingroup$ Was there given a reason for the requirement of normalization? It seems a strange thing to do with count data. Maybe used the (log of) total number of possible connections as an offset? with poisson/negbin? Search this site $\endgroup$ – kjetil b halvorsen Mar 5 at 11:11
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    $\begingroup$ There was no concrete reason. Something about standard deviation still being the same if you transformed it by z-scoring the count data? Made no sense to me. $\endgroup$ – 762 Mar 5 at 11:21
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    $\begingroup$ So there was probably no good reason, so don't do it! You might find something useful in this saved search $\endgroup$ – kjetil b halvorsen Mar 5 at 12:23
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In a larger network a person may have a chance to have more connections, but on the other hand they may not choose to - there is likely a saturation once the network gets above a certain size. You could look at the degree spectrum of each network separately - do these spectra change with network size? If so then the networks are not 'saturated' and it might be appropriate to scale the degree counts by some function of network size. You could choose a function that equalises the degree spectra.

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