That said, my main reference when thinking about communities is precisely your work on descriptive vs inferential approaches that you mention, so I will probably agree with you on most aspects :)

But at the same time, I think it's nice to keep in mind that there are situations where looking at disconnected components as a extreme case of communities can make sense, especially if the objective of the study is not to analyze data.

I completely agree, mixing two conceptualizations of community can lead to problems, because minimizing cut-sets and maximizing likelihoods are based on very different assumptions.

To be clear, I agree that interpreting community detection as a maximum-likelihood problem is a more powerful approach to understand complex datasets. My point is that, from a mathematical (not statistical) point of view, the other vision can be insightful too.

In fact, I would say the pure-math approach to communities tends to understand them as "almost disconnected" regions (partitions with a small cut-set), and this perspective has led to nice results (for example the Cheeger inequalities, the spectral clustering algorithms, perturbative methods, etc).

I think the interpretation of communities as network partitions with a small cut-set is useful in certain areas. Ofc, claiming that this conceptualization of community is statistically meaningful is problematic, but as a descriptive concept I think it's ok.

Ojalá un debate entre @lavacaesferica.bsky.social, @juanjosemillas.bsky.social y Arsuaga a raíz de la frase "si no conocemos las interacciones que ocurren en su interior, tampoco seremos capaces de predecir el comportamiento del sistema".