This paper proposes a network reconfiguration methodology for the three-phase unbalanced distribution system under both the normal operating and post-fault conditions. In normal operating condition, network reconfiguration is performed for real power loss minimization whereas, in the post-fault condition, reconfiguration is performed for faulty line isolation considering maximum demand should be met. Graph theory based method is used for maximum service restoration. A power flow algorithm is also developed to calculate power loss of unbalanced distribution systems. Proposed algorithm is implemented on IEEE 34-bus, and IEEE 123-bus unbalanced radial distribution systems under normal and faulty conditions and results demonstrate the effectiveness of the proposed method.