The electric power transmission network (EPTN) is a connected, geographically distributed network, which can be represented with a graph model with nodes and edges. The graph represents the physical connectivity of the EPTN. Deriving the graph model of the EPTN solely based on continually measured data is important for reliable power system operational situation awareness and decreasing uncertainties driven by weather, electrification, and interconnections. In this paper, an exhaustive search algorithm is presented to derive the EPTN graph model (TNGM) solely based on synchrophasor measurements retrieved from the substations without prior knowledge of the connectivity. Furthermore, an evaluation metric for any data-driven TNGM is introduced. The transmission network of the two-area, four-machine power system is used as the test system, and typical TNGMs for different power plant operating conditions are presented. Typical graphs obtained for network impedance and power flows are shown to be accurate, on average within 2% error margin.