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In the last few years, many studies in the cognitive and system neuroscience found that a consistent network of brain regions, referred to as the default network, showed high levels of activity when no explicit task was performed. Some scientists believed that the resting state activity might reflect some neural functions that consolidate the past, stabilize brain ensembles, and prepare us for the future. Here, we modeled the default network as undirected weighted graph, and then used graph theory to investigate the topological properties of the default network of the two groups of people with different intelligence levels. We found that, in both groups, the posterior cingulate cortex showed the greatest degree in comparison to the other brain regions in the default network, and that the medial temporal lobes and cerebellar tonsils were topologically separations from the other brain regions in the default network. More importantly, we found that the strength of some functional connectivities and the global efficiency of the default network were significantly different between the superior intelligence group and the average intelligence group, which indicates that the functional integration of the default network might be related to the individual intelligent performance.