Synchronous data-driven storytelling with network visualizations presents significant challenges due to the complexity of real-time manipulation of network components. While existing research addresses asynchronous scenarios, there is a lack of effective tools for live presentations. To address this gap, we developed TangibleNet, a projector-based AR prototype that allows presenters to interact with node-link diagrams using double-sided magnets during live presentations. The design process was informed by interviews with professionals experienced in synchronous data storytelling and workshops with 14 HCI/VIS researchers. Insights from the interviews helped identify key design considerations for integrating physical objects as interactive tools in presentation contexts. The workshops contributed to the development of a design space mapping user actions to interaction commands for node-link diagrams. Evaluation with 12 participants confirmed that TangibleNet supports intuitive interactions and enhances presenter autonomy, demonstrating its effectiveness for synchronous network-based data storytelling.