A method for metric ranking in invariant networks includes, given an invariant network and a set of broken invariants, two ranking processes are used to determine and rank the anomaly scores of each monitoring metrics in large-scale systems. Operators can follow the rank to investigate the root-cause in problem investigation. In a first ranking process, given a node/metric, the method determines multiple scores by integrating information from immediate neighbors to decide the anomaly score for metric ranking. In a second ranking process, given a node/metric, an iteration process is used to recursively integrate the information from immediate neighbors at each round to determine its anomaly score for metric ranking.