  For a graph representation of a dataset, a straightforward normality measure
for a sample can be its graph degree. Considering a weighted graph, degree of a
sample is the sum of the corresponding row's values in a similarity matrix. The
measure is intuitive given the abnormal samples are usually rare and they are
dissimilar to the rest of the data. In order to have an in-depth theoretical
understanding, in this manuscript, we investigate the graph degree in spectral
graph clustering based and kernel based point of views and draw connections to
a recent kernel method for the two sample problem. We show that our analyses
guide us to choose fully-connected graphs whose edge weights are calculated via
universal kernels. We show that a simple graph degree based unsupervised
anomaly detection method with the above properties, achieves higher accuracy
compared to other unsupervised anomaly detection methods on average over 10
widely used datasets. We also provide an extensive analysis on the effect of
the kernel parameter on the method's accuracy.
