Open source software vulnerabilities pose significant security risks to downstream applications. While vulnerability databases provide valuable information for mitigation, many security patches are released silently in new commits of OSS repositories without explicit indications of their security impact. This makes it challenging for software maintainers and users to detect and address these vulnerability fixes. There are a few approaches for detecting vulnerability-fixing commits (VFCs) but most of these approaches leverage commit messages, which would miss silent VFCs. On the other hand, there are some approaches for detecting silent VFCs based on code change patterns but they often fail to adequately characterize vulnerability fix patterns, thereby lacking effectiveness. For example, some approaches analyze each hunk in known VFCs, in isolation, to learn vulnerability fix patterns; but vulnerabiliy fixes are often associated with multiple hunks, in which cases correlations of code changes across those hunks are essential for characterizing the vulnerability fixes. To address these problems, we first conduct a large-scale empirical study on 11,900 VFCs across six programming languages, in which we found that over 70% of VFCs involve multiple hunks with various types of correlations. Based on our findings, we propose Fixseeker, a graph-based approach that extracts the various correlations between code changes at the hunk level to detect silent vulnerability fixes. Our evaluation demonstrates that Fixseeker outperforms state-of-the-art approaches across multiple programming languages, achieving a high F1 score of 0.8404 on average in balanced datasets and consistently improving F1 score, AUC-ROC and AUC-PR scores by 32.40%, 1.55% and 8.24% on imbalanced datasets. Our evaluation also indicates the generality of Fixseeker across different repository sizes and commit complexities.