In current industrial practice, thousands of industrial alarms generating millions of alarm events, are built into digital control systems typically found in power generation facilities, power grid and communication networks, oil refineries, petrochemical plants, and other manufacturing plants. Given the increasing complexity of such systems, an effective approach to managing alarms and the stream of data they generate becomes imperative. Hitherto, much of alarm management techniques are mostly rule-based with intensive engineering domain expertise requiring an understanding of the underlying physical processes and special skills on the part of the plant operator. This paper describes a novel graph-based data mining approach that can be used to analyze industrial alarm data. Our method leverages the availability of large timestamped historical alarm events datasets. Using these historical datasets, we developed a graph analytics model that identifies redundant alarms and the series of alarms associated with or leading to critical events. Our experiments using real-world (a power generation station and an oil refinery) industrial alarm datasets demonstrate that our proposed method is both scalable and efficient.