Opening and closing the eyes are a fundamental behavior for directing attention to the external versus internal world. However, it remains unclear whether the states of eyes-open (EO) relative to eyes-closed (EC) are associated with different topological organizations of functional neural networks for exteroceptive and interoceptive processing (processing the external world and internal state, respectively). Here, we used resting-state functional magnetic resonance imaging and neural network analysis to investigate the topological properties of functional networks of the human brain when the eyes were open versus closed. The brain networks exhibited increased cliquishness and increased local efficiency, but lower global efficiency during the EO state. Together, these properties suggest an increase in specialized information processing along with a decrease in integrated information processing in EO (vs. EC). More importantly, the "exteroceptive" network, including the attentional system (e.g., superior parietal gyrus and inferior parietal lobule), ocular motor system (e.g., precentral gyrus and superior frontal gyrus), and arousal system (e.g., insula and thalamus), showed higher regional nodal properties (nodal degree, efficiency and betweenness centrality) in EO relative to EC. In contrast, the "interoceptive" network, composed of visual system (e.g., lingual gyrus, fusiform gyrus and cuneus), auditory system (e.g., Heschl's gyurs), somatosensory system (e.g., postcentral gyrus), and part of the default mode network (e.g., angular gyrus and anterior cingulate gyrus), showed significantly higher regional properties in EC vs. EO. In addition, the connections across sensory modalities were altered by volitional eye opening. The synchronicity among visual system and motor, somatosensory and auditory system characteristics of EC was attenuated in EO, and the connections among visual system and attention, arousal and subcortical systems were increased in EO. These results may indicate that EO leads to a suppression of sensory modalities (other than visual) to allocate resources to exteroceptive processing. Our findings suggest that the topological organization of human brain networks dynamically switches corresponding to the information processing modes as we open or close our eyes.