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In this paper, we study the discrete differential calculus on hypergraphs byusing the Kouzul complexes. We define the constrained (co)homology forhypergraphs and give the corresponding Mayer-Vietoris sequences. We prove thefunctoriality of the Mayer-Vietoris sequences for the constrained homology andthe functoriality of the Mayer-Vietoris sequences for the constrainedcohomology with respect to morphisms of hypergraphs induced by bijective mapsbetween the vertices. Consequently, we obtain the Mayer-Vietoris sequences forthe constrained persistent (co)homology for filtrations of hypergraphs. Asapplications, we propose the constrained persistent (co)homology as a tool forthe computation of higher-dimensional persistent homology of large networks.

Differential Calculus on Hypergraphs and Mayer-Vietoris Sequences for the Constrained Persistent Homology