The identification of the instruments playing in a polyphonic music signal is an important and unsolved problem in Music Information Retrieval. In this paper, we propose a framework for the sound source separation and timbre classification of polyphonic, multi-instrumental music signals. The sound source separation method is inspired by ideas from Computational Auditory Scene Analysis and formulated as a graph partitioning problem. It utilizes a sinusoidal analysis front-end and makes use of the normalized cut, applied as a global criterion for segmenting graphs. Timbre models for six musical instruments are used for the classification of the resulting sound sources. The proposed framework is evaluated on a dataset consisting of mixtures of a variable number of simultaneous pitches and instruments, up to a maximum of four concurrent notes.