Complex network analysis applied to the resting brain has shown that sets of highly interconnected networks with coherent activity may support a default mode of brain function within a global workspace. Perceptual processing of environmental stimuli induces architectural changes in network topology with higher specialized modules. Evidence shows that during cognitive tasks, network topology is reconfigured and information is broadcast from modular processors to a connective core, promoting efficient information integration. In this paper, we explored how the brain adapts its effective connectivity within the connective core and across behavioral states. We used complex network metrics to identify hubs and proposed a method of classification based on the effective connectivity patterns of information flow. Finally, we interpreted the role of the connective core and each type of hub on the network effectiveness. We also calculated the complexity of electroencephalography microstate sequences across different tasks. We observed that divergent hubs contribute significantly to the network effectiveness and that part of this contribution persists across behavioral states, forming an invariant structure. Moreover, we found that a large quantity of multiple types of hubs may be associated with transitions of functional networks.