  Here we introduce connectivity operators, namely, diffusion operators,
general Laplacian operators, and general adjacency operators for hypergraphs.
These operators are generalisations of some conventional notions of apparently
different connectivity matrices associated with hypergraphs. In fact, we
introduce here a unified framework for studying different variations of the
connectivity operators associated with hypergraphs at the same time.
Eigenvalues and corresponding eigenspaces of the general connectivity operators
associated with some classes of hypergraphs are computed. Applications such as
random walks on hypergraphs, dynamical networks, and disease transmission on
hypergraphs are studied from the perspective of our newly introduced operators.
We also derive spectral bounds for the weak connectivity number, degree of
vertices, maximum cut, bipartition width, and isoperimetric constant of
hypergraphs.
