Graphs are a fundamental tool for modelling data in diverse real-world applications such as communication networks, traffic systems, and social networks. However, graph data is often distributed across multiple data owners and contains sensitive information, posing significant privacy concerns that impede collaborative analysis. This research aims to overcome these challenges by developing privacy-preserving solutions for graph analysis using the technique of secure multiparty computation (MPC). We review existing MPC-based approaches for privacy-preserving graph analysis, identifying their limitations in efficiency, scalability and adaptability. Furthermore, we present our results in enhancing privacy-preserving graph analysis and highlight the remaining challenges. We discuss potential strategies to overcome these challenges, including designing efficient primitives, leveraging different computational settings, and incorporating hardware accelerations to improve performance. Through these advancements, our research aims to make secure graph analysis both practical and widely applicable, ensuring privacy while enabling valuable insights from distributed graph data.