I am currently conducting a brain network analysis on my diffusion MRI data, using the connectomestats TFNBS algorithm. The final results that I get after running TFNBS are: beta0, beta1, enhanced, fwe_1mpvalue, null_contributions, null_dist, tvalue, uncorrected_pvalue, Zstat, abs_effect, cond, std_dev and std_effect.

Out of these results, I gathered that the relevant subnetwork could be identified using the fwe_1mpvalue file. Because having identical FWE-corrected p values demonstrate catagorisation by emergent effects in TFNBS, I was wondering if the edges represented by different, discrete p-values in the fwe-1mpvalue file can be separated out as independent subnetworks. For example, will all the edges with a p value equal to 0.0002 be a part of Subnetwork A, while all the edges with a p value equal to 0.0004 be a part of Subnetwork B?
Or, would it be more statistically accurate to look at the aggregate of all edges with a fwe-1m pvalue under a certain, higher threshold such as p<0.05? As an extension of the previous example, will all the edges with a p value equal to 0.0002 and 0.0004 be aggregated together into a single subnetwork, under a given p value threshold?

Furthermore, if we were to use TFNBS results in predicting the presence of a network correlating with a certain variable, would it be possible we use more statistically significant fwe-corrected p value thresholds such as p < 0.0005?

The TFNBS method derives a FWE-corrected p-value independently for each edge. Observing an identical p-value in multiple edges bears no greater consequence than would applying TFCE and observing an identical p-value in multiple voxels. Indeed if you were to increase both the number of permutations and the dh parameter, you would in almost all circumstances eventually break such equivalences. The reason why the p-value of 0.0002 is what you quote is because that’s the minimal achievable p-value when using the default of 5,000 permutations. So if two edges obtain that value, all that tells you is that there are multiple edges for which the enhanced statistic exceeds the maximal value observed in any edge in any random shuffling of the data; it provides no guarantee that those two edges even enhanced one another at all.

Indeed technically this is the case even for NBS. While it is true that all edges within a particular supra-threshold sub-network will all be assigned the same FWE-corrected p-value, since that value is calculated based on the number of edges within that sub-network (and that is by definition equivalent for all edges within that sub-network), it is not guaranteed that two edges with the same p-value are part of the same supra-threshold network. There could for example be two separate supra-threshold sub-networks of equivalent size to one another.

Or, would it be more statistically accurate to look at the aggregate of all edges with a fwe-1m pvalue under a certain, higher threshold such as p<0.05?

This is the standard mechanism for statistical inference. You pre-specify your alpha level of significance, and then identify any data for which the empirical p-value is smaller. 0.05 is the “default”, any reasonable value can be used; but it has to be pre-specified.