The complex dynamics of the Earth-atmosphere system across various spatial and temporal scales present significant challenges for weather prediction models. These models typically utilize discretized governing equations on grid points, incorporating physical schemes for scales smaller than the grid size to forecast future states. However, conventional error assessment metrics are inadequate for evaluating these models' performance. This research aims to contribute to the ongoing efforts to refine weather forecasting methodologies by integrating complex network analysis into error evaluation practices. This study introduces a novel metric based on networks constructed from reference temperature data (ERA5) and forecast data (GFS), focusing on a five-day temperature prediction at 2-meter level and at the 850 hPa pressure level. By calculating the time series correlation of temperature across grid points, networks are created based on correlation matrices and distance constraints. The proposed methodology employs Pearson correlation to evaluate the predictive accuracy of weather models. It establishes a threshold correlation of 0.96 for connecting grid points, while also considering points distances to limit connections. The resulting networks from observed and predicted data are compared using f-score metrics. The findings indicate that the model performs better in predicting correlations among closely located points, with accuracy diminishing as distance increases. However, the rate of accuracy decline varies across different model runs, suggesting that more reliable predictions exhibit a slower decrease in accuracy with increasing distance. Further, it is found that the structural error of the 850 hPa pressure level temperature indicates also the error on precipitation.