Thank you so much for this great, detailed explanation! If I'm interpreting what you said correctly, it sounds like path length for fcMRI data represents magnitude of correlations in a weighted graph, but is not the case in a binarized graph. I looked at the Rubinov and Sporns appendix, but again got an interpretation that generally describes path length as the distance between two nodes for an unweighted graph, which is still difficult for me to conceptualize in the arbitrary functional space, especially if magnitudes are binarized.

From looking at some output from Conn, the adjacency matrices only have values of 0 and 1. Does this indicate a binarized graph? If so, I read that 1 represents presence of an edge (so significant correlation between 2 ROIs) and 0 represents no edge (no significance achieved). For path length in this case then, would we say that a shorter path length means a value of 1 for the ROI pair (kind of like a direct association), whereas an increased path length would indicate a value of 0 between the direct ROI pair of interest, with higher values based on how many additional ROI-ROI comparisons were conducted until the initial ROIs had a common ROI with a significant correlation (indirect association)?

Again, thank you so much for taking the time to respond to my questions. It is incredibly helpful!!

Best,
Janelle