This chapter explores the intersection of network visualization, graph theory, and advanced computational techniques, focusing on how these elements converge to enhance our understanding of complex systems. We delve into various visualization algorithms, such as spring-embedded layouts and spectral methods, which translate abstract relationships into intuitive visual representations. Additionally, we highlight the significance of probabilistic graphical models in analyzing dependencies within networks. By bridging mathematical foundations with practical visualization strategies, this chapter aims to illuminate the intricate structures of networks, enabling deeper insights into their dynamics and applications across diverse fields, including social sciences, biology, and computer networks.