  We reveal a one-class homophily phenomenon, which is one prevalent property
we find empirically in real-world graph anomaly detection (GAD) datasets, i.e.,
normal nodes tend to have strong connection/affinity with each other, while the
homophily in abnormal nodes is significantly weaker than normal nodes. However,
this anomaly-discriminative property is ignored by existing GAD methods that
are typically built using a conventional anomaly detection objective, such as
data reconstruction. In this work, we explore this property to introduce a
novel unsupervised anomaly scoring measure for GAD, local node affinity, that
assigns a larger anomaly score to nodes that are less affiliated with their
neighbors, with the affinity defined as similarity on node
attributes/representations. We further propose Truncated Affinity Maximization
(TAM) that learns tailored node representations for our anomaly measure by
maximizing the local affinity of nodes to their neighbors. Optimizing on the
original graph structure can be biased by nonhomophily edges (i.e., edges
connecting normal and abnormal nodes). Thus, TAM is instead optimized on
truncated graphs where non-homophily edges are removed iteratively to mitigate
this bias. The learned representations result in significantly stronger local
affinity for normal nodes than abnormal nodes. Extensive empirical results on
10 real-world GAD datasets show that TAM substantially outperforms seven
competing models, achieving over 10% increase in AUROC/AUPRC compared to the
best contenders on challenging datasets. Our code is available at
https://github.com/mala-lab/TAM-master/.
