The brain is a highly nonlinear complex network system supporting diverse cognitive abilities. The locally segregated and globally integrated processing are the two basic foundations to cognition. However, how does the brain organizes the effective processing of neural information in the local and global scales, so as to support diverse cognitive tasks is not well understood. A physical hypothesis is that the brain system is in a dynamic critical state at rest and can support the balance of separation and integration. The modern network neuroscience (NNT) theory of human cognition propsoed that the brain’s flexible switching between local information processing (segregation) and global processing (integration) promotes the development of general intelligence, i.e., the segregation-integration balance corresponds to a higher general intelligence. However, there has been no clear evidence on whether the resting brain is in the segregation-integration balance at the whole-brain scale, and the NNT theory also urgently needs to be further verificated. We address the above open interdisciplinary question using an eigenmode-based approach to identify hierarchical modules in structural and functional brain networks. We further apply the hierarical mode analysis to functional network to quantify the functional segregation, integration and their balance. Meanwhile, we demonstrate that network segregation, integration and their balance in resting brains predict individual differences in diverse cognitive phenotypes. Our findings provide a systems level understanding of the brain’s functioning principles in supporting diverse functional demands and cognitive abilities, and advance modern network neuroscience theories of human cognition, which may shed light on dysfunctional segregation and integration in neurodegenerative diseases and neuropsychiatric disorders. Examples of application of the framework to stress and ADHD are briefly presented.