Phasor measurement units (PMUs) are being widely installed on power transmission systems, which provides a unique opportunity to enhance wide-area situational awareness. One key application is to utilize PMU data for real-time event identification. However, taking full advantage of all PMU data is still an open problem. This paper proposes a novel event identification method using multiple PMU measurements and deep graph learning techniques. Unlike previous models that rely on single PMU and ignore the interactive relationships between different PMUs or use multiple PMUs but determine the functional connectivity manually, our method performs datadriven interactive graph inference. Meanwhile, to ensure the optimality of the graph learning procedure, our method learns the interactive graph jointly with the event identification model. Moreover, instead of generating a single statistical graph to represent pair-wise relationships among PMUs during different events, our approach produces different event identificationspecific graphs for different power system events, which handles the uncertainty of event location. To test the proposed datadriven approach, a large real dataset from tens of PMU sources and the corresponding event logs have been utilized in this work. The numerical results validate that our method has higher identification accuracy compared to the previous methods.