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    So you think you have a power law - well isn’t that special and the papers linked therein is still one of the things I’m glad I found early in my career. It provides some ways to avoid the mistakes described in the OP.

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      To me, this is the key line in that paper:

      Ask yourself whether you really care. Maybe you don’t. A lot of the time, we think, all that’s genuine important is that the tail is heavy, and it doesn’t really matter whether it decays linearly in the log of the variable (power law) or quadratically (log-normal) or something else

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        That seems irrelevant at a glance, because it’s mainly about physics where there are natural limits to things. I thought power laws where much more characteristic of processes without natural limits, like file sizes, money owned, etc. I will still dig deeper into the papers linked there, because it’s highly relevant to me, I just want to hear your thoughts on the above.

        In part, OP seems to confirm my hypothesis: Twitter follows a power law, and Facebook only nearly does. But apparently Facebook also has a maximum connectedness of 5000! A truncated power law is obviously not a strict power law.

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          All of the stuff about statistical and analysis technique is completely relevant, and using poor technique is how we ended up with the situation the OP describes.

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            Page 22 of their paper describes the data sets they consider. Eyeballing it, about half are from the social sciences.

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              Yes! I have started reading the paper now and it’s almost exactly what I’ve been looking for in this area!

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            For other readers: the linked blog post in SteveH’s comment is by one of the authors of the paper and highlights several key takeaways. Recommended!