Complex systems from many areas such as biology, sociology, technology appear in form of large networks. These networks are represented usually in form of graphs and their structural properties are analyzed using the methods of graph theory. The so called Laplacian matrix became an important tool of spectral graph theory for the investigation of structural properties of large biological networks. Many important features of the underlying structure and dynamics of systems can be extracted from the analysis of the spectral density of graphs. The Laplacian matrices of empirical networks are unstructured large sparse matrices. The spectra of the Laplacian matrices of large protein-protein interaction networks (PPIN's) are computed using sparse eigenvalue solvers with high accuracy.