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The signal-to-interference-plus-noise-ratio performance of the multistage linear parallel and successive interference cancellers (LPIC and LSIC) in a long-code code-division multiple-access system is analyzed using a graphical approach. The decision statistic is modeled as a Gaussian random variable, whose mean and variance can be expressed as functions of moments of R for the LPIC and L for the LSIC, respectively, where R is the correlation matrix of signature sequences and L is the strict lower triangular part of R. Since the complexity of calculating these moments increases rapidly with the growth of the stage index, a graphical representation of moments is developed to facilitate the computation. Propositions are presented to relate the moment calculation problem to several well-known problems in graph theory, i.e., the coloring, the graph decomposition, the biconnected component finding, and the Euler tour problems. It is shown that the derived analytic results match well with simulation results.