Given the considerable scale of distribution networks in urban and rural areas, as well as the lack of management records, adjustments of switches during the distribution system operation are poorly documented. Such deficiency results in the inaccuracy of models stored in the distribution network automation system, and thus misleads the state estimation. With the emergence of information and communication technology, a large number of the feeder and residential smart meter data are accumulated. Such data can help recognize the operation modes of distribution networks by analyzing the relationships between the on/off states of switches and the voltage correlations among buses. However, the limited quantity and quality of the sampling data restrict the implementation of data-driven recognition. In this paper, a physical-probabilistic-network (PPN) model applied for inferring overall operation mode of distribution networks is proposed. Based on which, a belief propagation-based algorithm is proposed for the inference even under situations when there are only partial bus voltages data available. Meanwhile, the required variable for inference can be reduced from the active trail analysis. Experiment results are used to compare its performance with classic methods and to prove its effectiveness and advantages.