Outlier detection and identification are still important issues in the quality control of geodetic networks based on least squares estimation (LSE). In addition to existing network reliability measures, the paper proposes the LSE-based concept (together with the associated measures) of the Outlier-Exposing Potential (OEP) for Gauss-Markov models. The greater the model's redundancy, the more the configuration of its responses to gross errors exposes the location of these errors, and hence, the greater the model's OEP. The potential is given in the basic version and the extended version. The former considers only the effect of the model's redundancy, while the latter also considers the masking effect due to random observation errors at a specified magnitude of gross error. For models that have regions of unidentifiable errors, the corresponding OEP components have zero values. The reflection of OEP in the values of Minimal Identifiable Bias (MIB) is shown. It is proposed that OEP derived based on least squares adjustment be treated as a property of the model itself. The theory is illustrated on several 1D and 2D networks. The research is limited to models with uncorrelated observations and the case of a single gross error. These limitations enabled the formulation of clear properties of general character, not complicated by observation correlations and multiple-outlier combinations.