An emerging trend in AD research is brain network development including graphic metrics and graph mining techniques. To construct a brain structural network, Diffusion Tensor Imaging (DTI) in conjunction with T1 weighted Magnetic Resonance Imaging (MRI) can be used to isolate brain regions as nodes, white matter tracts as the edge, and the density of the tracts as the weight to the edge. To study such network, its sub-network is often obtained by excluding unrelated nodes or edges. Existing research has heavily relied on domain knowledge or single-Thresholding individual subject based network metrics to identify the sub network. In this research, we develop a bi-Threshold frequent subgraph mining method (BT-FSG) to automatically filter out less important edges in responding to the clinical questions. Using this method, we are able to discover a subgraph of human brain network that can significantly reveal the difference between cognitively unimpaired APOE-4 carriers and noncarriers based on the correlations between the age vs. network local metric and age vs. network or global metric. This can potentially become a brain network marker for evaluating the AD risks for preclinical individuals.