Spectral clustering tries to first find a lower dimensional representation of the data where it is better clustered after taking into account the inherent manifold structures. Next, any standard anomaly detector can be applied on the new representation. Although the python code has the implementation, the last step requires non-metric MDS transform and the scikit-learn implementation is not as good as R. Hence, use the R code (R/manifold_learn.R) for generating the transformed features.
For details, refer to: Supervised and Semi-supervised Approaches Based on Locally-Weighted Logistic Regression by Shubhomoy Das, Travis Moore, Weng-keen Wong, Simone Stumpf, Ian Oberst, Kevin Mcintosh, Margaret Burnett, Artificial Intelligence, 2013.