Let R be a ring and M be a right R-module. In this paper, we study about the small intersection graph of submodules of M. The small intersection graph \(\mathcal{S}\mathcal{I}_R(M)\) of M is the simple undirected graph with the non-trivial submodules of M as vertices and two distinct vertices N and K of M are adjacent if and only if \(N\cap K\) is a small submodule of M. First, we study some basic properties like connectedness and completeness of \(\mathcal{S}\mathcal{I}_R(M).\) Further, we study about \(\mathcal{S}\mathcal{I}_{\mathbb {Z}}(\mathbb {Z}_n)\) where n is not a prime number. In particular, we prove that \(\mathcal{S}\mathcal{I}_\mathbb {Z}(\mathbb {Z}_n)\) is weakly perfect.
