This paper aims to tackle the problem of brain network classification with machine learning algorithms using spectra of networks' matrices. Two approaches are discussed: first, linear and tree-based models are trained on the vectors of sorted eigenvalues of the adjacency matrix, the Laplacian matrix and the normalized Laplacian; next, SVM classifier is trained with kernels based on information divergence between the eigenvalue distributions. The latter approach gives promising results in the classification of autism spectrum disorder versus typical development and of the carriers versus noncarriers of an allele associated with the high risk of Alzheimer disease.