Separating the brain from the measurement

Neighbouring channels share optodes and scalp, so part of their correlation is not neural. Before reading the graph as brain organisation, check how much of it comes from the geometry of the probe and from channel quality.

Does connectivity simply follow distance?

Neighbouring channels can share an optode and sample overlapping scalp and tissue. Plot each pair's correlation against the distance between the channels.

Signal

Density

Distance of all channel pairs vs the edges kept in the graph (density above)

Correct for distance and look again

Two ways to check how much of the graph comes from distance, both at the same density:

Regress distance. Fit how connectivity falls with distance across all pairs, z_ij = a·e^−d_ij/λ + c, and build the graph from the residuals z_ij − f(d_ij): connectivity beyond what distance predicts.
Exclude short pairs. Ignore every pair closer than a minimum distance before thresholding. A stricter test.

Ignore pairs closer than

Question. Which measures depend most on short-range edges? Why does regressing distance change so little, while excluding short pairs changes more? What does that imply for “local” measures in channel space?

Channel pruning changes the graph

Keep the channels that quality control flagged (red outlines) and look at their degree.

Flagged channels become peripheral, weakly connected nodes. Keeping or removing them changes N, and differently in each subject, which is why group comparisons need a common node set.