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 𝑆𝐼𝑅(𝑀) of 𝑀 is the simple undirected graph with the nontrivial submodules of 𝑀 as vertices and two distinct vertices 𝑁 and 𝐾 of 𝑀 are adjacent if and only if 𝑁∩𝐾 is a small submodule of M. First, we study some basic properties like connectedness, diameter, girth and completeness of 𝑆𝐼𝑅(𝑀): Further, we study about 𝑆𝐼ℤ(ℤ𝑛) where n is not a prime number. In particular, we prove that 𝑆𝐼ℤ(ℤ𝑛) is weakly perfect.
