Characterization of a finite module with specified number of nontrivial submodules is one of the most important issues for researchers in module theory. In this paper, we will try to characterize a module with three or four nontrivial submodules by defining a new hypergraph on that module. Suppose that K is a module over a ring R. We introduce IHR(K) which we call intersection hypergraph of K. Any hyperedge in IHR(K), forms a complete subgraph of the complement of intersection graph of a module.Acharacterization of a finite modulewith exactly three nontrivial submodules via their associated hypergraphs are also presented. We provide a characterization of finite semisimple modules with exactly four nontrivial submodules in terms of their corresponded hypergraph. Some interesting examples are also included.
