Topology information is the foundation of advanced analysis functions in distribution network, such as power flow calculation, state estimation, and fault diagnosis. Due to the inability of some nodes in the low-voltage distribution network to upload their own operational status, the existence of these implicit nodes poses a huge challenge to topology identification. This paper proposes a topology identification method for low-voltage distribution networks based on latent tree model and cluster search. Firstly, a Bayesian network with embedded implicit nodes is proposed, which is defined as a latent tree model to provide probabilistic representation for all possible low-voltage distribution network topologies. Then a cluster search algorithm is proposed to generate candidate topologies, and the accuracy of the candidate topologies is evaluated using Bayesian information criteria. Finally, simulation and experiments are conducted to demonstrate the effectiveness and robustness of the proposed method.