Alzheimer's disease (AD) is a common neurodegenerative disease in the elderly, early diagnosis and timely treatment are very important to delay the course of the disease. In the past, most of the brain regions related to AD were identified based on the imaging method, which can only identify some atrophic brain regions. In this work, we used mathematical models to find out the potential brain regions related to AD. First, diffusion tensor imaging (DTI) was used to construct the brain structural network. Next, we set a new local feature index 2hop-connectivity to measure the correlation among different areas. The 2hop-connectivity utilizes the higher-order information of the graph structure relative to the traditional graph theory metrics. And for this, we proposed a novel algorithm named 2hopRWR to measure 2hop-connectivity. At last, we proposed a new index GFS (Global Feature Score) based on a global feature by combing 5 local features: degree centrality, betweenness centrality, closeness centrality, the number of maximal cliques, and 2hop-connectivity, to judge which brain regions are likely related to Alzheimer's Disease. As a result, all the top ten brain regions in the GFS scoring difference between the AD group and the non-AD group were related to AD by literature verification. Literature validation results comparing GFS with local features showed that GFS outperforms individual local features. Finally, the results of the canonical correlation analysis showed that the GFS was significantly correlated with the scores of the mini-mental state examination (MMSE) scale and the Montreal cognitive assessment (MoCA) scale. So, we believe the GFS can also be used as a new index to assist in diagnosis and objective monitoring of disease progression. Besides, the method proposed in this paper can be used as a differential network analysis method in other areas of network analysis.
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