Evolutions of hypergraphs and their embedded homology
Shiquan Ren, Chengyuan Wu, Jie Wu · arXiv (Cornell University) · 2018
Hypergraphs are higher-dimensional generalizations of graphs. An (abstract) simplicial complex is a hypergraph such that all the faces of hyperedges are still hyperedges. In [12], associated simplicial complexes of hypergraphs were defined and studied. And in [2], the embedded homology of hypergraphs was constructed and investigated. In this paper, we study the evolutions of hypergraphs as well as the induced changes of the embedded homology. We consider the lower-associated simplicial complex as an analog of the associated simplicial complex. The main result of this paper in- vestigates the changes of the embedded homology induced from evolutions of hypergraphs and the relations with the lower-associated simplicial complexes.