Summary: In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. We observe that, over a commutative ring, \(R, \mathbb{AG}_*(_RM)\) is connected, and \(\mathrm{diam}\mathbb{AG}_*(_RM)\leq 3\). Moreover, if \(\mathbb{AG}_*(_RM)\) contains a cycle, then \(\mathrm{gr}\mathbb{AG}_*(_RM)\leq 4\). Also for an \(R\)-module \(M\) with \(\mathbb{A}_*(M)\neq S(M)\backslash \{0\}\), \(\mathbb{A}_*(M)=\emptyset\) if and only if \(M\) is a uniform module and \(\mathrm{ann}(M)\) is a prime ideal of \(R\).