Recently, advanced sensing techniques ensure a large number of multivariate sensing data for intelligent fault diagnosis of machines. Given the advantage of obtaining accurate diagnosis results, multi-sensor fusion has long been studied in the fault diagnosis field. However, existing studies suffer from two weaknesses. First, the relations of multiple sensors are either neglected or calculated only to improve the diagnostic accuracy of fault types. Second, the localization for multi-source faults is seldom investigated, although locating the anomaly variable over multivariate sensing data for certain types of faults is desirable. This article attempts to overcome the above weaknesses by proposing a global method to recognize fault types and localize fault sources with the help of multi-sensor relations (MSRs). First, an MSR model is developed to learn MSRs automatically and further obtain fault recognition results. Second, centrality measures are employed to analyze the MSR graphs learned by the MSR model, and fault sources are therefore determined. The proposed method is demonstrated by experiments on an induction motor and a centrifugal pump. Results show the proposed method’s validity in diagnosing fault types and sources.