Cables are ubiquitous in modern vehicles and the rate of failures has grown with the complexity of the vehicular communication network. The severity of the faults in cables begins in a mild manner, known as soft faults, where the network is still able to perform its required functions. Such faults if not caught in early stages, may develop into hard/severe faults which can lead to serious breakdowns of the whole system. It is thus of prime importance to design and implement an efficient soft fault detection system. In this paper, a bus Ethernet network composed of one source and multiple receivers is studied. A soft fault, which may be caused by a localized degradation of the cable quality, is equivalent to an additional series resistor. Since all the receivers are linked to the same line (the backbone), a fault in the network may affect all the receivers which make it difficult to pinpoint the faulty branch. The transmission transfer function measured between the source and each end of line is monitored. A new health indicator inspired from the classical chain matrix model of the cables is proposed. This indicator is computed at each receiver to detect a soft fault and to locate the faulty branch. Based on the studied topology, a signature matrix is generated, which will be used for fault detection and localization. Simulation results are presented to illustrate our approach.