Online social networks (OSNs) are threatened by Sybil attacks, which create fake accounts (also called Sybils) on OSNs and use them for various malicious activities. Therefore, Sybil detection is a fundamental task for OSN security. Most existing Sybil detection methods are based on the graph structure of OSNs, and various methods have been proposed recently. However, although almost all methods have been compared experimentally in terms of detection performance and noise robustness, theoretical understanding of them is still lacking. In this study, we show that existing graph-based Sybil detection methods can be interpreted in a unified framework of low-pass filtering. This framework enables us to theoretically compare and analyze each method from two perspectives: filter kernel properties and the spectrum of shift matrices. Our analysis reveals that the detection performance of each method depends on how well low-pass filtering can extract low frequency components and remove noisy high frequency components. Furthermore, on the basis of the analysis, we propose a novel Sybil detection method called SybilHeat. Numerical experiments on synthetic graphs and real social networks demonstrate that SybilHeat performs consistently well on graphs with various structural properties. This study lays a theoretical foundation for graph-based Sybil detection and leads to a better understanding of Sybil detection methods.