Graph can be represented by 1) square incidence matrix (whose dimension is the number of vertices) or 2) list or adjacency lists.
My question is - is there such simple representation (e.g. by matrix or tensors) for the simplicial complexes (https://en.wikipedia.org/wiki/Simplicial_complex). I can imagine that there can be vector of incidence matrices (one for each concrete face) in which there is some "canonical" way to order faces/matrices so that the representation is unique.
Mostly I am interested in the use of such representation for the research of evolution of graphs and simplicial complexes. Graph evolution is just operation/transformation on the incidence matrix. But I am not sure how can I express operator/transformation on the simplicial complex?