In a subnetwork analysis, the connectome is split into subnetworks and differences between the two groups are explored for each or a selection of them. The decomposition into subnetworks can be done according to previous knowledge, which brings interesting properties as it can be based on a functional decomposition of the brain as the default mode network, the sensory network, visual network, etc.... The decomposition can also be performed in an automatic way, according to graph theory algorithms as the K-core decomposition, or the multi-level optimization of modularity, which brings other interesting properties. Finally, it can also be based on the p-values of an uncorrected local analysis as described by Zalesky.
As for the global analysis, a summary statistic condensating a given subnetwork property is used. The summary statistic is computed for the S subnetworks of all the subjects, and S statistical tests are performed to compare the subnetworks between the two groups. Here, given the S tests performed, correction methods cannot be discarded, mostly if several summary statistics are explored (in this case, S*SM tests are performed, where SM is the number of tested summary statistics).
However, testing on subnetworks consciderably increases the power of the test compared to single connections analysis, as the number of tests is lower and therefore the correction procedures are more tolerant.