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Objective In the current study we investigated topological abnormalities of the cerebral white matter networks in narcolepsy type 1 (NT1) patients and its relationship with their cognitive abnormalities using diffusion tensor imaging (DTI) technology. Methods DTI and the Beijing version of the Montreal Cognitive Assessment (MoCA-BJ) were applied to 30 NT1 patients and 30 age-matched healthy controls. DTI studies were also carried using the 3T MRI system. Next, DTI data was used to establish a cerebral white matter network for all subjects and graph theory was applied to analyze the topological characteristics of the white matter structural network. Topographical parameters (such as local efficiency (Eloc), global efficiency (Eglob) and small-world (σ)) between NT1 patients and controls were then compared. The correlation between MoCA-BJ scores and topological parameters was also analyzed. Results MoCA-BJ scores in NT1 patients were lower than those in the healthy controls. Compared with healthy controls, the global efficiency of the white matter network and attributes of the small world network were significantly reduced in NT1 patients. Finally, the global efficiency of the white matter structural network was related to the MoCA-BJ score of NT1 patients. Conclusion The abnormal topological characteristics of the white matter structural network in NT1 patients may be associated with their cognitive impairment.