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?
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).