Motivation: Gene regulatory network (GRN) inference is a complex task aiming to unravel regulatory interactions between genes in a cell. A major shortcoming of most GRN inference methods is that they do not attempt to find the optimal sparsity, i.e. the single best GRN, which is important when applying GRN inference in a real situation. Instead, the sparsity tends to be controlled by an arbitrarily set hyperparameter. Results: In this paper, two new methods for predicting the optimal sparsity of GRNs are formulated and benchmarked on simulated perturbation-based gene expression data using four GRN inference methods: LASSO, Zscore, LSCON, and GENIE3. Both sparsity prediction methods are defined using the hypothesis that the topology of real GRNs is scale-free, and are evaluated based on their ability to predict the sparsity of the true GRN. The results show that the new topology-based approaches reliably predict a sparsity close to the true one. This ability is valuable for real-world applications where a single GRN is inferred from real data. In such situations, it is vital to be able to infer a GRN with the correct sparsity.