Networks in sectors like telecommunications and transportation often contain sensitive user data, requiring privacy enhancing technologies during data release to ensure privacy. While Differential Privacy (DP) is recognized as the leading standard for privacy preservation, its use comes with new challenges, as the noise added for privacy introduces inaccuracies or biases. DP techniques have also been found to distribute these biases disproportionately across different populations, inducing fairness issues.This paper investigates the effects of DP on bias and fairness when releasing network edge weights. We specifically examine how these privacy measures affect decision-making tasks, such as computing shortest paths, which are crucial for routing in transportation and communications networks, and provide both theoretical insights and empirical evidence on the inherent trade-offs between privacy, accuracy, and fairness for network data release.