Outlier detection in networks with missing links

Outliers arise in networks due to different reasons such as fraudulent behaviour of malicious users or default in measurement instruments and can significantly impair network analyses. In addition, real-life networks are likely to be incompletely observed, with missing links due to individual non-response or machine failures. Therefore, identifying outliers in the presence of missing links is a crucial problem in network analysis. A new algorithm is introduced to detect outliers in a network and simultaneously predict the missing links. The proposed method is statistically sound: under fairly general assumptions, this algorithm exactly detects the outliers, and achieves the best known error for the prediction of missing links with polynomial computational cost. The sub-linear convergence of the algorithm is proven, which confirms its computational efficiency. A simulation study is provided, which demonstrates the good behaviour of the algorithm in terms of outlier detection and prediction of the missing links. The method is also illustrated with an application in epidemiology and with the analysis of a political Twitter network. The algorithm is freely available as an R package on the Comprehensive R Archive Network.