In energy or communication networks, cables are omnipresent. Like any other systems, they are subject to faults. Faults in cables are divided into two families : soft faults and hard faults. Soft faults are faults that do not affect the data and/or energy transfer. However, over time they tend to turn into hard faults that can lead to a total system breakdown. In this paper, we focus on the detection of soft faults and the localization of the faulty branch in star-shaped networks. The proposed method is based on the comparison between a network Reference Transmission Coefficient (RTC) and a TC measured online through power line communication using Orthogonal Frequency Division Multiplexing (OFDM) scheme. Our proposal is discussed for both energy and communication networks. Simulation-based results are presented that confirm the ability of the method to locate the faulty branches.