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Many papers[1, 2] related to power laws say that alpha values between 2 and 3 are common in real networks. I understand that this means the mean is finite and the variance is infinite, but I do not have an intuitive understanding as to why this is should be a common feature in real networks.

BadProgrammer
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  • It porbably falls closer to cross validated, or perhaps even psychology, than here. The data comes from, e.g., income distribution, internet page links, paper citations, etc., which are all man-made, so it is really a question why humans create networks that appears to be described by a power law with those alphas (although as your other link demonstrates, it might just be trendy to claim a power law). – user10354138 May 13 '19 at 12:29
  • I don't think it's true that power-laws typically come from man made distributions. Seems like there are many examples from astronomy, physics, biology etc. on wikipedia – BadProgrammer May 14 '19 at 07:24
  • Kepler's third law, square-cube law, etc. are not about probability distributions. – user10354138 May 14 '19 at 07:29
  • The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares,[2] the foraging pattern of various species,[3] the sizes of activity patterns of neuronal populations,[4] the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms,[5] the sizes of power outages, criminal charges per convict, volcanic eruptions,[6] human judgements of stimulus intensity[7][8] and many other quantities.[9] – BadProgrammer May 14 '19 at 07:36
  • The link should have been to Empirical Examples – BadProgrammer May 14 '19 at 07:37

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