In network science, numerous studies based on the complementarity principle have emerged
since 2018 [1]. Unfortunately, theoretical foundations of complementarity are still in their infancy. Recently, a synthetic complementarity-based model called Complementarity Random
Hyperbolic Graph (CRHG) has been proposed. CRHG model was assumed to explain the topological properties of real complementarity-driven networks. In other words, this model could serve as a foundation for studying complementarity mechanisms in networks.The main goal of this thesis is to address the knowledge gap: although a complementarity-based network model has been proposed in previous studies, its topological properties have not been systematically examined. To fill in this gap, this work systematically studies complementarity network models (CRHG, GCRHG) and documents their topological properties. Moreover, we interpret the topological properties as a function of the network model parameters. We find that the CRHG model exhibits three fundamental properties: Scale-Free property, Small-World property, and Non-vanishing bipartite clustering. It indicates that it is a unique combination compared to other synthetic models. Its unique complementary connectivity mechanism makes it particularly effective for modelling complex networks formed by the complementarity mechanism. Furthermore, we also study and investigate a generalized synthetic model called Generalized Complementarity Random Hyperbolic Graph (GCRHG). We measure and analyze its clustering and bipartite clustering properties. We find that this model allows for smooth turning between similarity and complementarity. Overall, we document and interpret the topological properties of simulations for complementarity-based spatial graph models. Additionally, we conduct partial simulation verification of the theoretical topological properties of synthetic complementarity-based models, providing a reference for their future development and applications.