To analyze a network of conductors, especially an electrical power supply network, it is planned to measure the spectral (49) and temporal (50) nature of a signal available at a node of the network. An image (49 51) representing this state is produced. This image produced is compared with an expected image (52 55) showing an <> state of one and/or the other of the appliances connected to this network. The state of the appliances, whether on or off, is deduced therefrom. This information can be used to optimize the use of the electrical power or to monitor the activity of the appliances concerned.