  In this study, we explore the substructures of a hypergraph that lead us to
linearly dependent rows (or columns) in the incidence matrix of the hypergraph.
  These substructures are closely related to the spectra of various hypergraph
matrices, including the signless Laplacian, adjacency, Laplacian, and adjacency
matrices of the hypergraph's incidence graph. Specific eigenvectors of these
hypergraph matrices serve to characterize these substructures. We show that
vectors belonging to the nullspace of the adjacency matrix of the hypergraph's
incidence graph provide a distinctive description of these substructures.
Additionally, we illustrate that these substructures exhibit inherent
similarities and redundancies, which manifest in analogous behaviours during
random walks and similar values of hypergraph centralities.
