The clinical manifestation of Lewy body dementia (DLB) is distinct from Alzheimer's disease (AD), but overlap with Parkinson's disease dementia (PDD). However, little is known about different topology properties of abnormal brain networks associated with these neurodegenerative diseases. In order to study the difference of brain networks in various dementia subtypes, we used $^{\mathbf {18}}\text{F}$-Fluorodeoxyglucose positron emission tomography ($^{\mathbf {18}}\text{F}$-FDG PET) images and graph theory methods to investigate altered whole-brain intrinsic glucose metabolic functional networks in three Chinese dementia groups compared to healthy control (HC) group, including 22 AD patients, 18 PDD patients, 22 DLB patients and 22 HC subjects from Huashan Hospital, Shanghai, China. The experimental results disclosed that in the three dementia groups, compared to HC group, the small-world characteristics were lost. Additionally, compared with HC group, the clustering coefficients of three dementia groups were higher; the characteristic path lengths were longer. In terms of local efficiency and global efficiency, it was at the lowest level in DLB group. We also found differences about distributions of hub regions amongst the four groups. This finding could further help physicians to understand pathological mechanisms of different dementia.