Quantum metrology takes advantage of nonclassical resources such as entanglement to achieve a sensitivity level below the standard quantum limit. To date, almost all quantum-metrology demonstrations are restricted to improving the measurement performance at a single sensor, but a plethora of applications require multiple sensors that work jointly to tackle distributed sensing problems. Here, we propose and experimentally demonstrate a reconfigurable sensor network empowered by continuous-variable (CV) multipartite entanglement. Our experiment establishes a connection between the entanglement structure and the achievable quantum advantage in different distributed sensing problems. The demonstrated entangled sensor network is composed of three sensor nodes each equipped with an electro-optic transducer for the detection of radio-frequency (RF) signals. By properly tailoring the CV multipartite entangled states, the entangled sensor network can be reconfigured to maximize the quantum advantage in distributed RF sensing problems such as measuring the angle of arrival of an RF field. The rich physics of CV multipartite entanglement unveiled by our work would open a new avenue for distributed quantum sensing and would lead to applications in ultrasensitive positioning, navigation, and timing.