Given an IP source-destination traffic network, how do we spot mis-behavioral IP sources (e.g., port-scanner)? How do we find strange users in a user-movie rating graph? Moreover, how can we present the results intuitively so that it is relatively easier for data analysts to interpret? We propose NrMF, a non-negative residual matrix factorization framework, to address such challenges. We present an optimization formulation as well as an effective algorithm to solve it. Our method can naturally capture abnormal behaviors on graphs. In addition, the proposed algorithm is linear wrt the size of the graph therefore it is suitable for large graphs. The experimental results on several data sets validate its effectiveness as well as efficiency. Copyright © SIAM.