A consistent survey on anomaly detection and description is provided in this paper. This topic is extremely relevant due to the wide range of application domains. For this same reason, this topic is difficult to exhaustively address with a completely general focus, as the application-specific character makes most key concepts dependent on concrete scopes and goals.

The added value with respect to other surveys is evident in the title, which clearly orients potential readers toward graph-based solutions(which are extensively described in the paper). Despite its relatively long length, the paper is readable and suitable for a large audience, probably due to its continuous use of examples, as well as the basic definitions given, which will be appreciated by many readers.

This is definitely a solid and interesting contribution. I have just two (minor) observations to make: there are parts of the paper that would benefit from a more concise focus, and the last section of the paper is devoted to real-world applications. That is very interesting and well-though-out. In my opinion, however, it would have been better if these topics were covered in two different papers: one with a more theoretical focus and another dealing with an application-oriented analysis.