SBM and three vertex scenario

[edunnwe1]

A few lectures ago, we talked about the fact that SBM fails for a situation like the Bock paper where you want to do statistics on three vertex interactions. I was wondering, though: rather than needing to scrap the SBM, what if you reconstructed the graph instead to summarize this three vertex interaction as an interaction between vertices? For example, what if the vertices were excitatory neurons, and they shared an edge if they synapsed onto the same inhibitory neuron?

More generally, does it make sense to construct the graph on a data set in a few different ways to assess different questions? Do you run into confounds by doing this?

[DSP137]

Interesting proposition. I'm not sure how this would work, at least in the example given (granted I haven't thought of a better idea). If we put an edge between excitatory neurons only if they synapse onto the same inhibitory neuron, would the fact that neurons can have up to thousands of synapses cause a problem?

[ghost]

I think whenever you construct graphs, you might get different features based on the definitions you build the graph on. So you may get confounds, but you might also verify something else. I don't see a problem to constructing graphs in different ways and getting confounds either, because that could potentially lead to something interesting.

Also, since brain data is hard to acquire, aren't data sets used in many different studies? This might be off topic from answering your Bock paper question, since that's about different ways of constructing graphs for one study...