Impact of sample size when using exponential random graph modeling I am working on revising a manuscript centered on identifying the drivers behind certain types of student interaction. One critique that I'm having trouble addressing is that they are worried about my sample size in comparison to other studies that have used exponential random graph modeling (ERGM) to identify these factors. I've looked around, but can't find any arguments against using ERGMs on small networks.
As such, does anyone know if there is a "minimum" sample size for exponential random graph modeling and, if so, could you provide references I could read through? Thanks!
 A: As with all things statistics a small sample maybe a problem because (1) you will have too much uncertainty in your estimates or (2) the "statistical machinery" breaks because some asymptotic results do not hold.
With all things network it is more complicated because it is not immediately clear what is the sample size? Number of nodes or the number of ties? (hint: it turns out it's both are important but each for a different thing).
From the practical point of view if your networks are large enough for the MCMC estimation of an ERGM to work well, then your estimates are valid and the "small sample size" will be reflected in standard errors, p-values etc. If  MCMC won't work because of network size you can turn to exact methods (see Vega Yon below) and get valid results too.
Recommended references:

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*Krivitsky & Kolaczyk On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry https://doi.org/10.1214%2F14-STS502

*Vega Yon et al Exponential random graph models for little networks https://doi.org/10.1016/j.socnet.2020.07.005
