  In this paper, we study the discrete differential calculus on hypergraphs by
using the Kouzul complexes. We define the constrained (co)homology for
hypergraphs and give the corresponding Mayer-Vietoris sequences. We prove the
functoriality of the Mayer-Vietoris sequences for the constrained homology and
the functoriality of the Mayer-Vietoris sequences for the constrained
cohomology with respect to morphisms of hypergraphs induced by bijective maps
between the vertices. Consequently, we obtain the Mayer-Vietoris sequences for
the constrained persistent (co)homology for filtrations of hypergraphs. As
applications, we propose the constrained persistent (co)homology as a tool for
the computation of higher-dimensional persistent homology of large networks.
