  Despite the fact that many important problems (including clustering) can be
described using hypergraphs, theoretical foundations as well as practical
algorithms using hypergraphs are not well developed yet. In this paper, we
propose a hypergraph modularity function that generalizes its well established
and widely used graph counterpart measure of how clustered a network is. In
order to define it properly, we generalize the Chung-Lu model for graphs to
hypergraphs. We then provide the theoretical foundations to search for an
optimal solution with respect to our hypergraph modularity function. Two simple
heuristic algorithms are described and applied to a few small illustrative
examples. We show that using a strict version of our proposed modularity
function often leads to a solution where a smaller number of hyperedges get cut
as compared to optimizing modularity of 2-section graph of a hypergraph.
