  A large number of studies on Graph Outlier Detection (GOD) have emerged in
recent years due to its wide applications, in which Unsupervised Node Outlier
Detection (UNOD) on attributed networks is an important area. UNOD focuses on
detecting two kinds of typical outliers in graphs: the structural outlier and
the contextual outlier. Most existing works conduct experiments based on
datasets with injected outliers. However, we find that the most widely-used
outlier injection approach has a serious data leakage issue. By only utilizing
such data leakage, a simple approach can achieve state-of-the-art performance
in detecting outliers. In addition, we observe that existing algorithms have a
performance drop with the mitigated data leakage issue. The other major issue
is on balanced detection performance between the two types of outliers, which
has not been considered by existing studies. In this paper, we analyze the
cause of the data leakage issue in depth since the injection approach is a
building block to advance UNOD. Moreover, we devise a novel variance-based
model to detect structural outliers, which outperforms existing algorithms
significantly and is more robust at kinds of injection settings. On top of
this, we propose a new framework, Variance based Graph Outlier Detection
(VGOD), which combines our variance-based model and attribute reconstruction
model to detect outliers in a balanced way. Finally, we conduct extensive
experiments to demonstrate the effectiveness and efficiency of VGOD. The
results on 5 real-world datasets validate that VGOD achieves not only the best
performance in detecting outliers but also a balanced detection performance
between structural and contextual outliers.
