The authors investigate the structure of the generalized total graph \(GT_{H}(R)\) where \(R\) is a commutative ring with a nonzero identity element and \(H\) is a nonempty proper subset of \(R\) such that \(R\setminus H\) is a saturated multiplicatively closed subset of \(R\). In case where \(H\) is a prime ideal of \(R\), a complete description of \(GT_{H}(R)\) is given and the diameter and girth of the graphs \(GT_{H}(H)\), \(GT_{H}(R\setminus H)\) and \(GT_{H}(R)\) are determined. In case where \(H\) is not an ideal of \(R\), the authors prove that \(GT_{H}(H)\) is always connected but never complete and its diameter is \(2\). Moreover, \(GT_{H}(H)\) and \(GT_{H}(R\setminus H)\) are never disjoint subgraphs of \(GT_{H}(R)\) and \(|H|\geq 3\). Also if \(GT_{H}(R\setminus H)\) is connected, then so is \(GT_{H}(R)\). The paper closes with a description of the generalized total graph \(GT_{H}(R)\) for some specific rings, namely when \(R\) is either an idealization or a \(D+M\) construction or a localization.