I'd rather not rename plot_simulated_connectome, as I don't see the need to commit to sparse estimators for the example on simulated connectomes.

With regards to the other examples, agreed that it's a mess. Indeed the didactic values of the 2 examples are not well separated. Also, there is plot_signal_extraction that goes a bit in the same direction, even though it is on a hard parcellation, rather than a probabilistic atlas.

They bring a variety of teaching:

• How to extract signals on a probabilistic parcellation and build a correlation matrix
• The importance of defining good confounds (plot_signal_extraction is good for that)
• The difference between correlation and inverse covariance
• How to do things at the group level: it's a "for" loop, but that tends to be a difficulty for the beginners.

I wonder if it's a good thing to put in the same example the single subject and the group analysis. I would rather merge the one with the probabilistic parcellation and the one with the hard parcellation.

We should rename the multi-subject one to a name that makes it very clear that it's purpose is to illustrate multi-subject. For instance a file name "plot_multi_subject_connectomes" and a title "Computing connectomes on multiple subjects".

Ok.
What I can do for all examples (except ICA and Dictionary learning, cause I am a stranger to that) is to synthesize in a table what they demo piece by piece, to see usefulness and overlaps.
I also have a question: is there any reason we rely only on ADHD for examples ? for advanced connectomes examples we can rely on COBRE/ABIDE to avoid the signal extraction part

However, in the long run, I think that I would like to try to have all examples running with the cobre data.

You would keep ADHD only to demo signal extraction ?

AFAIK, ADHD dataset is more used than COBRE and there has been a competition on it so people in the field are more likely to know it.

I did a table with the connectivity examples, except those ICA and dictionary learning related.
I hope it is useful.

I added a secondary teaching box to group demoed features/explanations that may be additional to the example purpose. I tried to separate nilearn API specific teaching from more general functional connectivity teaching, because some users can be beginners in FC.

So from what I read I have some little changes suggestions
1- consolidate functional connectivity section 3.1. Extracting times series to build a functional connectome. For me we jump too fast to subtle things sparse inverse related. I suggest

• adding a paragraph about preprocessing, explaining that various possibilities exist and are illustrated through the examples.
• adding a paragraph about the NiftiSpheresMasker

2- In section 3.2.Connectome extraction: inverse covariance for direct connections adding once for all an explanation for the link covariance/correlation/precision/partial correlation.

3- Standardization is a hidden process to use covariance as a correlation. May be we can expose cov_to_corr and prec_to_partial

4- following previous discussions, decide whether or not ConnectivityMeasure is used only for multiple subjects and be consistent

5- fix ADHD changing TR across the examples

6- Why systematically use the first figure in gallery ? For instance for the seed-to-voxel correlations it would be beautiful to see the correlation map, instead of a timeseries.

7- We can merge probabilistic/determinsitic/DMN spheres examples, it would be an example with all the various maskers.

and I have a question: what are the guidelines for examples writing style ? For the moment they are a mix of compact minimalistic phrasing (eg the probabilistic atlas extraction) and more detailed structured examples (eg the seed-to-voxel example).