With a finite R-module M we associate a hypergraph CIHR(M) having the set V of vertices being the set of all nontrivial submodules of M. Moreover, a subset Ei of V with at least two elements is a hyperedge if for K, L in Ei there is K ∩ L 6= 0 and Ei is maximal with respect to this property. We investigate some general properties of CIHR(M), providing condition under which CIHR(M) is connected, and find its diameter. Besides, we study the form of the hypergraph CIHR(M) when M is semisimple, uniform module and it is a direct sum of its each two nontrivial submodules. Moreover, we characterize finite modules with three nontrivial submodules according to their cointersection hypergraphs. Finally, we present some illustrative examples for CIHR(M).
