Fast vulnerability root cause analysis is crucial for patching vulnerabilities and has always been a hotspot in academia and industry. The existing vulnerability root cause analysis methods based on the statistical feature analysis of a large number of test sample execution records have problems such as random noise and missing important logical correlation instructions. According to the test set measurement in this study, the proportion of random noise in the existing statistical methods reaches more than 61%. To solve the above problems, this study proposes a vulnerability root cause analysis method based on the local path graph, which extracts vulnerability-related information such as the inter-function call graph and intra-function control flow transfer graph from the execution paths. The local path graph is utilized for eliminating irrelevant instruction (i.e., noise instructions) elimination, constructing the logic relations for vulnerability root cause relevant points, and adding missing critical instructions. An automated root cause analysis system for binary software, LGBRoot, has been implemented. The effectiveness of the system has been evaluated on a dataset of 20 public CVE memory corruption vulnerabilities. The average time for single-sample root cause analysis is 12.4 seconds. The experimental data show that the system can automatically eliminate 56.2% of noise instructions, and mend as well as visualize the 20 logical structures of vulnerability root cause relevant points, speeding up the vulnerability analysis of analysts.