A global analysis aims to reveal major differences in the network properties. Such changes are expected to be reflected in a single network summary statistic as the clusterness, the mean degree, the efficiency, etc.... Each summary statistic recapitulates a different aspect of the network.
In this analysis, the summary statistic is computed for each subject, and a statistical test for mean difference is performed between the two populations.
Multiple summary statistics can be tested to explore changes that might be reflected in different ways. Note that correction for multiple comparisons should theoretically be applied in this case in order to control the false discovery rate, but most reported studies do not follow this recommendation as the number of test is usually low.