Dear CONN experts, 

I would like to apply graph theory for task-based functional connectivity, i.e., connectivity related to the difference between 2 frequencies of muscle vibration (60Hz and 20 Hz). I am thus interested in connectivity during 60 Hz that "goes above" 20 Hz.
I have a network of 20 ROIs. I specified both stimulus conditions (60 Hz, 20 Hz), as well as rest blocks (no stimulus) at the first-level (onsets and durations of blocks) and included stimulus conditions as confounds during Denoising (as well as motion parameters, CSF, WM).

I would like to calculate graph theoretical measures of the contrast of 60 Hz - 20 Hz in my subject group ("patients", n=20). Therefore, I selected patients,  contrast [1] in the between-subject contrast field, and 60 Hz and 20 Hz, contrast [1 -1] in the between-conditions contrast field. After clicking Graph Theory, specifying my desired adjacency matrix threshold and clicking Export data, CONN saves a .csv file, a two .mat files (xxx.networkmeasures, xxx.stats). When opening the .csv file, I noticed I have 40 rows, with different graph theoretical measures for the network, and for each ROI. I assume that the rows 1:20 contain graph measures for my 20 patients for condition 60 Hz, and that rows 21:40 contain the same measures for condition 20Hz. Is this correct?

However, I am specifically interested in calculating graph measures on the difference in connectivity between both conditions. Can I obtain this by calculating "difference matrices" per subject, i.e., by subtracting their correlation matrix at 60 Hz and correlation matrix at 20 Hz, and apply graph theory analysis on these difference matrices?

Thank you for your help, 

Kind regards, 
Nina

Dear Nina,

That is a good question, what CONN typically does (e.g. when you select both conditions in the Second-level Results tab and enter a [1 -1] contrast in the 'between-conditions contrast' field before clicking on the 'Graph theory' button) is to compute separately the connectivity graphs for each of your two conditions (and of course also separately for each subject), then compute the measure of interest (e.g. global efficiency) for each of these graphs separately, and last enter those measures of interest into your desired second-level model (e.g. paired t-test comparing global efficiency across your two  conditions). The T- statistics reported in the graph-theory results explorer window correspond to that test (e.g. paired t-test) for the network-level measures (e.g. is global efficiency of the entire graphs/networks different between the two stimulus conditions?; this is reported in the results list first row bolded and labeled 'network'), as well as separately for each ROI/node within those networks (e.g. is global efficiency of each ROI/node different between the two stimulus conditions?; this is reported in the results list rows as a separate analysis for each ROI)

If you want to replicate these same analyses from the results in the .csv file, simply enter those 40 values (for each column in the csv file) into a paired t-test (first 20 samples should correspond to 20 subjects / first condition, and last 20 samples should corresopnd to 20 subjects / second condition)

All of this focuses on calculating between-condition differences in graph measures. If, on the other hand, you are interested in calculating graph measures of between-condition-difference networks, the closest thing to that would be to use Network-Based Statistics (Zalesky et al., also available in conn as part of ROI-to-ROI results explorer). That will compute the difference between your two stimulus conditions separately for every edge/connection, then it will threshold those edges using a user-defined threshold (e.g. uncorrected p<.001 values) to form a "graph of between-condition differences", and then it will compute the cost of those graphs (other graph measures are not yet available/implemented) and determine its significance using randomization/permutation analyses.

To do that in conn, within the ROI-to-ROI second-level results tab enter your second-level model (just the same as before) and now click on the 'results explorer' button (instead of the 'graph theory' button), click on the 'select all' button to look at the entire network of ROI-to-ROI connections (or select your desired set of ROIs manually), then enter your desired network-forming threshold (e.g. unc-p=0.001) in the 'connection-level threshold' field, and last enable the 'seed/network' threshold, enable permutation tests, and select 'network-intensity (NBS)' and your desired false-positive control level (e.g. p-FDR=0.05)

Hope this helps
Alfonso
Originally posted by Nina Goossens:

Dear Alfonso, 

Thank you for your quick response and help!

I have two follow-up questions.

1) I am also interested in whether two groups (patients and controls) differ in terms of connectivity related to the difference between my conditions. I think I can determine this with NBS as well, following the instructions you described above (select both groups, contrast [1 -1], select both conditions [1 -1], hit results explorer, etc)? Can I also use this to determine whether graph measures of the between-condition-difference are correlated with a behavioral measure?

2) Wen selecting both groups  [1 -1]  and both conditions [1 -1], clicking graph theory, specifying edge threshold and desired p-value, I found a difference in global efficiency in paracentral lobule-ROI (PCL_R). Now, the .csv file contained 80 rows (row 1:20 patients 60 Hz, row 21:40 controls 60 Hz, row 41:60 patients 20 Hz, row 61:80 controls 20 Hz). I noticed that when I calculated the difference in global efficiency in PCL_R for condition 60 Hz - 20 Hz, and then performed a two-sample t-test on this difference, I got the same result as provided by the "graph theory" table. 
However, I struggle a bit with the question whether this represents a between-group difference in' global efficiency related to the difference of 60Hz - 20Hz' (of interest), or whether this represents a between-group difference in between-condition differences in global efficiency (cfr. bold text in your response)? 

Kind regards, 
Nina