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Is there a widely accepted alternative to Erdos-Renyi random graphs that addresses their issues with 1) degree distributions not having heavy enough tails and 2) clustering coefficients being too low?

My understanding is that Barabasi-Albert models for example don’t work as well as one would like for this purpose and that there have been a number of misleading results with them. What else is there? For example, do stochastic block models fix the clustering and degree distribution issues?

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    $\begingroup$ What is "heavy enough" tails, and what is "too low"? What is "this purpose"? $\endgroup$ – Henning Makholm Mar 31 at 13:12
  • $\begingroup$ In a sense, you're looking for alternatives to Barabasi–Albert. The Erdős–Rényi model is not a model for statisticians: it is primarily a tool for probabilistic combinatorics, in which setting we don't care about heavy tails and low clustering coefficients. $\endgroup$ – Misha Lavrov Mar 31 at 17:41
  • $\begingroup$ @Henning “Heavy enough” meaning able to handle complex networks with skewed degree distributions. ”This purpose” is producing a generative model for a network that might have a skewed degree distribution $\endgroup$ – JohnDoeVsJoeSchmoe Apr 1 at 0:45
  • $\begingroup$ @Misha Thank you for that distinction, I didn’t know that. Is there a type of network you’d suggest for statisticians looking for a generative model for a complex network that could have a skewed degree distribution? $\endgroup$ – JohnDoeVsJoeSchmoe Apr 1 at 0:47
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See here for info on graphs with a "power-law degree distribution" (degree distributions not having heavy enough tails). Also this on the "preferential attachment model" (satisfies both the properties you are after).

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  • $\begingroup$ Preferential attachment was already mentioned in the question, though of course you might disagree with the summary given. $\endgroup$ – Misha Lavrov Mar 31 at 17:39
  • $\begingroup$ @JRyan I’ve seen that Wikipedia page. Are all those models “generative”? $\endgroup$ – JohnDoeVsJoeSchmoe Apr 1 at 0:49
  • $\begingroup$ @JohnDoeVsJoeSchmoe the preferential attachment model is generative $\endgroup$ – JRyan Apr 1 at 19:53
  • $\begingroup$ I know that it generates the model in a procedural way, but would you describe the resulting model as generative? In the sense that it suggests a probability distribution that can be used to simulate data (edges)? $\endgroup$ – JohnDoeVsJoeSchmoe Apr 1 at 20:47
  • $\begingroup$ No, It is apparently a mechanistic model (see tuvalu.santafe.edu/~aaronc/courses/7000/…) $\endgroup$ – JRyan Apr 2 at 18:47

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