In this paper, we give a description of spectral clustering methods where data is represented by a weighted graph. In spectral clustering, the goal is to find the partition that has the smallest spectral cut, which is a measurement of how well the data are divided into groups for some partition. Three spectral clustering methods obtained by gradual generalization are presented, the method of minimizing the spectral normalized cut of a bipartition in an undirected graph, the method of minimizing the spectral normalized cut of a partition in an undirected graph, and the method of minimizing the spectral weighted cut of a partition in a directed graph. All three methods of minimizing spectral cuts are derived similarly. First, we represent the minimization problem of a spectral cut in matrix form and relax that discrete minimization problem in order to reduce it to the problem of Rayleigh quotients minimization, which gives us the solution to the relaxed continuous minimization problem of a spectral cut. We then find an approximate solution to the initial discrete minimization problem by clustering the rows in the relaxed solution matrix as points in \( \R^k \) using the \( k \)-means algorithm. In the last chapter, the implementation of algorithms for these methods is given, and examples are shown on which these algorithms were tested.