  The purpose of this paper is to introduce a model to study structures which
are widely present in public transportation networks. We show that, through
hypergraphs, one can describe these structures and investigate the relation
between their spectra. To this aim, we extend the structure of $(m,k)$-stars on
graphs to hypergraphs: the $(m,k)$-hyperstars on hypergraphs. Also, by giving
suitable conditions on the hyperedge weights we prove the existence of matrix
eigenvalues of computable values and multiplicities, where the matrices
considered are Laplacian, adjacency and transition matrices. By considering
separately the case of generic hypergraphs and uniform hypergraphs, we prove
that two kinds of vertex set reductions on hypergraphs with $(m,k)$-hyperstar
are feasible, keeping the same eigenvalues with reduced multiplicity. Finally,
some useful eigenvectors properties are derived up to a product with a suitable
matrix, and we relate these results to Fiedler spectral partitioning on the
hypergraph.
