Title: Structural Privacy in Graphs. Abstract: Graph Neural Networks (GNNs) gained popularity to address the tasks over the graph-structured data that best represent many real-world systems. The privacy of the participants of these systems is at risk if the GNNs are not carefully designed. Existing works in privacy-preserving GNNs primarily ensure the privacy of features and labels of a node. In order to ensure complete privacy related to graph data, its structure also needs to be privatized. We provide a method SPGraph to privatize the graph structure by adding noise to the neighborhood data of the node. Our method addresses two challenges in introducing structural privacy in graphs. Applying randomization on the set of actual neighbors to introduce noise leads to a reduction in the degree of a node, which is undesirable. To overcome this first challenge, we introduce $\lambda$-selector that samples nodes to be added to the set of neighbors. The second challenge is to denoise the neighborhood so that the noise added in the neighborhood does not significantly impact the accuracy. In this view, we use $p$-hop neighborhood to compensate for the loss of actual neighbors in the randomization. We continue to use the node and label privacy as implemented in the previous methods for privacy in GNNs. We conduct extensive experiments over real-world datasets to show the impact of perturbation in the graph structure. 