In this paper, we introduce the small intersection graph of ideals of a lattice L, denoted by SG(L), in which the vertex set is being the set of all non-trivial ideals of L, and two distinct vertices I and J are adjacent if I∧J ≪ L. We study basic properties of SG(L). Also, we investigate the properties of SG(L) as connectivity, diameter, grith and orthogonal vertices.
