Clustering analysis is one of the main tools for exploratory data analysis, with applications from statistics, image processing, biology to social sciences. Generally, it isue data process to and meaning ful structure, explanatory underlying processes and generative features. Its goal is to group set of objects in such a way that objects in the same group (clusters) are similar to each other (insomesense) whilst objects from different clusters are dissimilar. One way to perform clustering analysis is to look at data asagraph, then clustering becomes a graph cutting problem. Within this set of techniques, Spectral Clustering stands for its simplicity and great performance. Recently, a new approach [12] radically diferent from spectral clustering has emerged and it consists on learning agraph that has the desired properties, namely, that it has the desired number of connected components or clusters. In this thesis we have explored these techniques and we have proposed new ones with the goal of designing an eficient algorithm that can exploit the additional information in directed graphs, with respect to achieve good clustering performance. Experimental results on synthetic data sets exhibitthe efectiveness of the proposed methods.