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Traditional models often rely on simplifying assumptions that overlook the complexity of real-world contact patterns. In this study, we present an extended Bayesian framework that integrates genomic, temporal, and network data to reconstruct transmission networks with greater accuracy. By incorporating network structure as a prior, the model accounts for social and spatial proximity, allowing transmission probabilities to vary with contact or social distance. We further enhance inference sensitivity through a hypothesis testing procedure optimized via constrained likelihood estimation. Simulation results demonstrate that network-informed models outperform non-network-informed models, particularly under limited genetic resolution. Application to a tuberculosis dataset from Kampala, Uganda reveals that the network-informed model resolves transmission ambiguities more effectively than models based solely on genetic and temporal data. Additionally, Exponential Random Graph Model (ERGM) analysis indicates that transmission is more likely to occur through weak social ties than within tightly connected clusters, aligning with sociological theories of information flow. While the framework shows strong performance, limitations such as data sparsity and computational demands remain. Future work will focus on integrating mobility data to further refine transmission inference. 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